Skip to main content
Back to DIFFERENTIAL EQUATIONS

Your Progress

0 / 452 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • DIFFERENTIAL EQUATIONS

Differential equations practice · Medium

Choose an answer to check it, or open “View answer” to study the explanation. Sign in to save progress to your account.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →
Showing 301-330 of 452 questions

Preparing practice and saved progress…

301 Medium
301 of 452
Application +4 | -1
The general solution of y2dx+(x2−xy+y2)dy=0y^2 d x+\left(x^2-x y+y^2\right) d y=0, is
View answer and explanation
Correct option: D
log⁡y=tan⁡−1yx+C\log y=\tan ^{-1} \frac{y}{x}+C
The correct answer is D (log⁡y=tan⁡−1yx+C\log y=\tan ^{-1} \frac{y}{x}+C) because it is the solution obtained by solving the given homogeneous differential equation using the substitution y=vxy=vx.
302 Medium
302 of 452
Application +4 | -1
If y=y(x)y=y(x) is the solution curve of the differential equation (x2−4)dy−(y2−3y)dx=0,\left(x^2-4\right) d y-\left(y^2-3 y\right) d x=0, x>2,x>2, y(4)=32y(4)=\frac{3}{2} and the slope of the curve is never zero, then the value of y(10)y(10) equals:
View answer and explanation
Correct option: A
31+(8)14\frac{3}{1+(8)^{\frac{1}{4}}}
Option A (31+(8)14\frac{3}{1+(8)^{\frac{1}{4}}}) is correct because it is the value of y(10) obtained after solving the differential equation and applying the given initial condition.
303 Medium
303 of 452
Application +4 | -1
The solution of the differential equation ydx+xdyydx−xdy=x2exyy4\frac{y d x+x d y}{y d x-x d y}=\frac{x^2 e^{x y}}{y^4} satisfying y(0)=1y(0)=1, is
View answer and explanation
Correct option: B
x3=3y3(1−e−xy)x^3=3 y^3\left(1-e^{-x y}\right)
Option B (x3=3y3(1-e(-xy))) is correct because it is the solution to the differential equation that satisfies the initial condition y(0)=1.
304 Medium
304 of 452
Application +4 | -1
A particular solution of log⁡dy dx=4x+5y,y(0)=0\log \frac{\mathrm{d} y}{\mathrm{~d} x}=4 x+5 y, \quad y(0)=0 is given by
View answer and explanation
Correct option: A
5e4x+4e−5y=95 e^{4 x}+4 e^{-5 y}=9
The correct answer is A (5e4x+4e−5y=95 e^{4 x}+4 e^{-5 y}=9) because it is the particular solution to the given differential equation with the initial condition y(0)=0.
305 Medium
305 of 452
Application +4 | -1
The differential equation dydx=1−y2y\frac{{dy}}{{dx}} = \frac{{\sqrt {1 - {y^2}} }}{y} determines a family of circles with
View answer and explanation
Correct option: C
Fixed radius 1 and variable centres along the xx-axis
Option C (Fixed radius 1 and variable centres along the xx-axis) is correct because the general solution represents a family of circles with radius 1 and centers on the x-axis.
306 Medium
306 of 452
Application +4 | -1
The integrating factor of the differential equation dydx+y(1−x)x=1−x\frac{{dy}}{{dx}} + \frac{y}{{\left( {1 - x} \right)\sqrt x }} = 1 - \sqrt x is
View answer and explanation
Correct option: B
1+x1−x\frac{{1 + \sqrt x }}{{1 - \sqrt x }}
Option B (1+x1−x\frac{{1 + \sqrt x }}{{1 - \sqrt x }}) is correct because it is the integrating factor of the given differential equation.
307 Medium
307 of 452
Application +4 | -1
The general solution of the differential equation xdy+ydx+2x3dx=0x d y+y d x+2 x^3 d x=0, is
View answer and explanation
Correct option: B
xy+12x4=Cx y+\frac{1}{2} x^4=C
Option B (xy+12x4=Cx y+\frac{1}{2} x^4=C) is correct because it is the general solution obtained by integrating the given differential equation.
308 Medium
308 of 452
Application +4 | -1
For y=cos⁡kxy=\cos k x to be a solution of differential equation d2ydx2+4y=0\frac{d^2 y}{d x^2}+4 y=0, the value of kk is
View answer and explanation
Correct option: A
2
Option A (2) is correct because substituting y = cos(kx) into the differential equation and solving for k yields k = 2.
309 Medium
309 of 452
Application +4 | -1
The solution of the differential equation x+ydydx=2yx+y \frac{d y}{d x}=2 y is
View answer and explanation
Correct option: B
log⁡(y−x)=c+xy−x\log (y-x)=c+\frac{x}{y-x}
Option B (log⁡(y−x)=c+xy−x\log (y-x)=c+\frac{x}{y-x}) is the correct solution of the given differential equation, which is solved by substituting y=vxy=vx.
310 Medium
310 of 452
Application +4 | -1
The equation of the curve in which the portion of yy-axis cut off between the origin and the tangent varies as the cube of the abscissa of the point of contact is
View answer and explanation
Correct option: C
y=−kx32+cxy = - \frac{{k{x^3}}}{2} + c\mathrm{ }x
Option C (y=−kx32+cxy = - \frac{{k{x^3}}}{2} + c\mathrm{ }x) is correct because it is the solution to the differential equation formed based on the given condition about the y-intercept of the tangent.
311 Medium
311 of 452
Application +4 | -1
The general solution of the differential equation ydy+1+y2dx=0y d y+\sqrt{1+y^2} d x=0 represents a family of
View answer and explanation
Correct option: C
Hyperbolas
Option C (Hyperbolas) is correct because the general solution of the given differential equation represents a family of hyperbolas.
312 Medium
312 of 452
Application +4 | -1
The solution of dydx=xlog⁡x2+xsin⁡y+ycos⁡y\frac{{dy}}{{dx}} = \frac{{x\log {x^2} + x}}{{\sin y + y\cos y}} is
View answer and explanation
Correct option: A
ysin⁡y=x2log⁡x+cy\sin y = {x^2}\log x + c
Option A (ysin⁡y=x2log⁡x+cy\sin y = {x^2}\log x + c) is correct because it is the solution obtained after separating variables and integrating the differential equation.
313 Medium
313 of 452
Application +4 | -1
Let y=y(x)y=y(x) be the solution of the differential equation (2xlog⁡ex)dydx+2y=3xlog⁡ex,x>0\left(2 x \log _e x\right) \frac{d y}{d x}+2 y=\frac{3}{x} \log _e x, x > 0 and y(e−1)=0y\left(e^{-1}\right)=0. Then, y(e)y(e) is equal to
View answer and explanation
Correct option: C
−3e-\frac{3}{\mathrm{e}}
Option C (-3/e) is correct because it is the value of y(e) obtained by solving the given differential equation with the given initial condition.
314 Medium
314 of 452
Analyzing +4 | -1
The order of the differential equation whose general solution gives by y=(c1+c2)cos⁡(x+c3)−c4ex+c5y=\left(c_1+c_2\right) \cos \left(x+c_3\right)-c_4 e^{x+c_5} where c1,c2,c3,c4,c5\mathrm{c}_1, \mathrm{c}_2, \mathrm{c}_3, \mathrm{c}_4, \mathrm{c}_5 are arbitrary constants is
View answer and explanation
Correct option: B
3
Option B (3) is correct because the general solution can be simplified to have only three independent arbitrary constants.
315 Medium
315 of 452
Application +4 | -1
The solution of x3dydx+4x2tan⁡y=exx^3 \frac{d y}{d x}+4 x^2 \tan y=e^x sec yy satisfying y(1)=0y(1)=0 is
View answer and explanation
Correct option: C
tan⁡y=(x−1)exx−3\tan y=(x-1) e^x x^{-3}
Option D (sin⁡y=ex(x−1)x−3\sin y=e^x(x-1) x^{-3}) is correct because it satisfies the given differential equation and the initial condition y(1)=0y(1)=0.

Explore Other Chapters in MATHEMATICS

View All →
SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
316 Medium
316 of 452
Application +4 | -1
Let y=y(x)y=y(x) be the solution of the differential equation (1+x2)dydx+y=etan⁡−1x,y(1)=0\left(1+x^2\right) \frac{d y}{d x}+y=\mathrm{e}^{\tan ^{-1} x}, y(1)=0. Then y(0)\mathrm{y}(0) is
View answer and explanation
Correct option: B
12(1−eπ/2)\frac{1}{2}\left(1-\mathrm{e}^{\pi / 2}\right)
Option A (12(1−eπ/2)\frac{{1}}{{2}}(1 - e^{\pi/2})) is correct because it is the value of y(0) obtained by solving the given differential equation with the given initial condition.
317 Medium
317 of 452
Application +4 | -1
If the differential equation dydx=yx+ϕ(xy)\frac{d y}{d x}=\frac{y}{x}+\phi\left(\frac{x}{y}\right) has the general solution y=xlog⁡∣cxy=\frac{x}{\log \mid c x}, then ϕ(xy)=……\phi\left(\frac{x}{y}\right)=\ldots \ldots
View answer and explanation
Correct option: D
−y2x2\frac{-y^2}{x^2}
Option D (−y2x2\frac{{-y^2}}{{x^2}}) is correct because it satisfies the given differential equation and general solution after substitution and differentiation.
318 Medium
318 of 452
Application +4 | -1
Solution of the differential equation dydxtan⁡y=sin⁡(x+y)+sin⁡(x−y)\frac{{dy}}{{dx}}\tan y = \sin \left( {x + y} \right) + \sin \left( {x - y} \right) is
View answer and explanation
Correct option: A
sec⁡y+2cos⁡x=c\sec y + 2\cos x = c
Option A (sec⁡y+2cos⁡x=c\sec y + 2\cos x = c) is correct because it is the solution to the given differential equation.
319 Medium
319 of 452
Application +4 | -1
The solution of dydx+1=ex+y\frac{{dy}}{{dx}} + 1 = {e^{x + y}} is
View answer and explanation
Correct option: A
e−(x+y)+x+c=0{e^{ - \left( {x + y} \right)}} + x + c = 0
Option A (e−(x+y)+x+c=0{e^{ - \left( {x + y} \right)}} + x + c = 0) is correct because it is the solution obtained by solving the given differential equation using a substitution.
320 Medium
320 of 452
Application +4 | -1
y=cx−c2y = cx - {c^2}, is the general solution of the differential equation
View answer and explanation
Correct option: A
(y′)2−xy′+y=0{\left( {y'} \right)^2} - xy' + y = 0
Option A ((y′)2−xy′+y=0{\left( {y'} \right)^2} - xy' + y = 0) is correct because it is obtained by eliminating the arbitrary constant 'c' from the given general solution.
321 Medium
321 of 452
Application +4 | -1
The solution of y′+y=−xyy^{\prime}+y=-\frac{x}{y} is given by
View answer and explanation
Correct option: C
y2=−x+12(1+e−2π)y^2=-x+\frac{1}{2}\left(1+e^{-2 \pi}\right)
The correct answer is C (y2=−x+12(1+e−2π)y^2=-x+\frac{{1}}{{2}}\left(1+e^{-2 \pi}\right)) because it is the solution of the given differential equation with the initial condition y(0)=1.
322 Medium
322 of 452
Application +4 | -1
Differential equation of y=sec⁡(tan⁡−1x)y = \sec ({\tan ^{ - 1}}x) is
View answer and explanation
Correct option: C
(1+x2)dydx=xy\left( {1 + {x^2}} \right)\frac{{dy}}{{dx}} = xy
Option C ((1+x2)dydx=xy\left( {1 + {x^2}} \right)\frac{{dy}}{{dx}} = xy) is correct because it is the differential equation derived from the given equation.
323 Medium
323 of 452
Application +4 | -1
If dydx=cos⁡(x+y),y(π2)=0\frac{d y}{d x}=\cos (x+y), y\left(\frac{\pi}{2}\right)=0, then y(0)=y(0)=
View answer and explanation
Correct option: D
−2tan⁡−1(π2−1)-2 \tan ^{-1}\left(\frac{\pi}{2}-1\right)
Option D (−2tan⁡−1(π2−1)-2 \tan ^{-1}\left(\frac{\pi}{2}-1\right)) is correct because it is the solution obtained after solving the given differential equation with the initial condition.
324 Medium
324 of 452
Understanding +4 | -1
The differential equation of all straight lines passing through origin is
View answer and explanation
Correct option: D
None of these
The correct answer is None of these because the differential equation represents the family of straight lines passing through the origin is y=xdydxy = x \frac{{dy}}{{dx}}.
325 Medium
325 of 452
Application +4 | -1
The differential equations of all circles passing through origin and having their centres on the x\mathrm{x}-axis is
View answer and explanation
Correct option: D
dydx=y2−x22xy\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{y^2-x^2}{2 x y}
Option D (dydx=y2−x22xy\frac{{\mathrm{{dy}}}}{{\mathrm{{dx}}}} = \frac{{y^2-x^2}}{{2 x y}}) is correct because it represents the differential equation of all circles passing through the origin and having their centers on the x-axis.
326 Medium
326 of 452
Application +4 | -1
The solution of the differential equation sec⁡2xtan⁡ydx+sec⁡2ytan⁡xdy=0{\sec ^2}x\tan ydx + {\sec ^2}y\tan xdy = 0 is
View answer and explanation
Correct option: A
tan⁡ytan⁡x=c\tan y\tan x = c
Option A (tan⁡ytan⁡x=c\tan y\tan x = c) is correct because it is the solution obtained by separating variables and integrating the given differential equation.
327 Medium
327 of 452
Application +4 | -1
The solution of the differential equation dydxtan⁡y=sin⁡(x+y)+sin⁡(x−y)\frac{{dy}}{{dx}}\tan y = \sin \left( {x + y} \right) + \sin \left( {x - y} \right) is
View answer and explanation
Correct option: A
sec⁡y+2cos⁡x=c\sec y + 2\cos x = c
Option A (sec⁡y+2cos⁡x=c\sec y + 2\cos x = c) is correct because it is the result of integrating the given differential equation after separation of variables and using trigonometric identities.
328 Medium
328 of 452
Application +4 | -1
The solution of dy=cos⁡x(2−ycosecx)dxdy = \cos x\left( {2 - y\mathrm{cosec}x} \right)dx, where y=2y = \sqrt 2, when x=π4x = \frac{\pi }{4} is
View answer and explanation
Correct option: A
y=sin⁡x+12cosecxy = \sin x + \frac{1}{2}\mathrm{cosec}x
Option A (y=sin⁡x+12cosecxy = \sin x + \frac{1}{2}\mathrm{cosec}x) is correct because it satisfies the given differential equation and the initial condition y=2y = \sqrt 2 when x=π4x = \frac{\pi }{4}.
329 Medium
329 of 452
Application +4 | -1
The solution of dydx=ax+gby+f\frac{{dy}}{{dx}} = \frac{{ax + g}}{{by + f}} represents a circle when
View answer and explanation
Correct option: B
a=−ba = - b
Option B (a=−ba = - b) is correct because the given differential equation represents a circle only when the coefficients of x2x^2 and y2y^2 are equal in magnitude and opposite in sign.
330 Medium
330 of 452
Application +4 | -1
The motion of a particle is given by dxdt=\frac{d x}{d t}= −3acos⁡2tsin⁡t,dydt=3asin⁡2tcos⁡t-3 a \cos ^2 t \sin t, \frac{d y}{d t}=3 a \sin ^2 t \cos t and passes through at tt =0=0, then the path is given by
View answer and explanation
Correct option: D
(x+a)2/3+y2/3=a2/3(x+a)^{2 / 3}+y^{2 / 3}=a^{2 / 3}
The correct answer is D ((x+a)2/3+y2/3=a2/3(x+a)^{2 / 3}+y^{2 / 3}=a^{2 / 3}) because it represents the path of the particle given the parametric equations and initial condition.
Revision notes and key takeaways

Review DIFFERENTIAL EQUATIONS in your textbook or class notes, then use this set to check your understanding.

Showing 301-330 of 452 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - DIFFERENTIAL EQUATIONS MCQs (All) 975 MCQs → ENGINEERING MATHEMATICS - DIFFERENTIAL EQUATIONS MCQs (Easy) 494 MCQs → ENGINEERING MATHEMATICS - DIFFERENTIAL EQUATIONS MCQs (Hard) 29 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → MATRICES 1363 MCQs → INDEFINITE INTEGRATION 1179 MCQs

Your practice

0 / 452 answered · 452 remaining · 0% accuracy

Progress is stored on this device. Sign in to save to your account.

✓ Correct · ✗ Incorrect · ○ Unanswered

Practice settings

Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →