JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Observe the following statements

A:Interating factor of

\frac{{dy}}{{dx}} + y = {x^2}

{e^x}

R: Integrating factor of

\frac{{dy}}{{dx}} + P\left( x \right)y = Q\left( x \right)

{e^{\int P\left( x \right)dx}}

Then, the true statement among the following is

View answer and explanation

Correct option: C

A is true, R is true,

\mathrm{R} \Rightarrow \mathrm{A}

Option C (A is true, R is true,

\mathrm{R} \Rightarrow \mathrm{A}

) is correct because both the integrating factor for the given equation and the general formula for the integrating factor are correct, and the general formula implies the specific case.

More Questions from DIFFERENTIAL EQUATIONS

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Let

y=y(x)

be the solution of the differential equation

\left(3 y^{2}-5 x^{2}\right) y d x+2 x\left(x^{2}-y^{2}\right) d y=0

such that

y(1)=1

. Then

\left|(y(2))^{3}-12 y(2)\right|

is equal to : The degree and order of the differential equation whose solution is a parabola whose axis is

x

-axis, are If

{x^2} + {y^2} = 1

, then

\left( {y' = \frac{{dy}}{{dx}},y'' = \frac{{{d^2}y}}{{d{x^2}}}} \right)

x = A\cos 4t + B\sin 4t,

then

\frac{{{d^2}x}}{{d{t^2}}}

is equal to Let

y=y_{1}(x)

and

y=y_{2}(x)

be the solution curves of the differential equation

\frac{d y}{d x}=y+7

with initial conditions

y_{1}(0)=0

and

y_{2}(0)=1

respectively. Then the curves

y=y_{1}(x)

and

y=y_{2}(x)

intersect at Let

y=y(t)

be a solution of the differential equation

\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}

where,

\alpha>0, \beta>0

and

\gamma>0

. Then

\lim \limits_{{x \rightarrow \infty}} y(t)