Differential equations practice · Medium

The solution of the differential equation $\frac{d y}{d x}=\frac{1}{x y\left[x^2 \sin y^2+1\right]}$ is

The solution of the differential equation $\left( {{x^2} - y{x^2}} \right)\frac{{dy}}{{dx}} + {y^2} + x{y^2} = 0$ is

The solution of the differential equation $\left( {2y - 1} \right)dx - \left( {2x + 3} \right)dy = 0$, is

The general solution of the differential equation $\left(x-y^2\right) d x+y\left(5 x+y^2\right) d y=0$ is :

If a curve passing through $(1,1)$ satisfies the differential equation $x^2 d y=y^2 d x+x y d(x y)$, then the equation of the curve is

General solution of the differential equation $(x \log x) \frac{d y}{d x}+y=\frac{2}{x} \log x$ is

The solution of the differential equation $\frac{y d x+x d y}{y d x-x d y}=\frac{x^2 e^{x y}}{y^4}$ satisfying $y(0)=1$, is

If $y\left( t \right)$ is a solution of $\left( {1 + t} \right)\frac{{dy}}{{dt}} - ty = 1\,$ and $y\left( 0 \right) = - 1$, then $y\left( 1 \right)$ is equal to

The solution of the differential equation $x\frac{{dy}}{{dx}} + y = x\cos x + \sin x$, given that $y = 1$ when $x = \frac{\pi }{2}$, is

The differential equation representing the family of ellipses having foci either on the $x$-axis or on the $y$-axis, centre at the origin and passing through the point $(0,3)$ is :

The solution of the differential equation $(x+y-1) d x-(2 x+2 y-3) d y=0$ is $\ldots \ldots$..

The order of the differential equation associated with the primitive $y = {c_1} + {c_2}{e^x} + {c_3}{e^{ - 2x + {c_4}}}$, where ${c_1},{c_2},{c_3},{c_4}$ are arbitrary constants, is

Let $\alpha x=\exp \left(x^{\beta} y^{\gamma}\right)$ be the solution of differential equation $2 x^{2} y d y-\left(1-x y^{2}\right) d x=0, x>0$, $y(2)=\sqrt{\log _{e} 2}$. Then $\alpha+\beta-\gamma$ equals

Solution of the differential equation $\frac{d y}{d x}+y \sec ^2 x=\tan x \sec ^2 x$ is

Solution of the differential equation $\frac{{dy}}{{dx}} + \frac{y}{x} = \sin x$ is

The curve such that the initial ordinate of any tangent is less than the abscissa of the point of tangency by two unit is

If $y=y(x)$ is the solution curve of the differential equation $\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \frac{\pi}{3}, y(0)=1$, then $y\left(\frac{\pi}{6}\right)$ is equal to

Form of the differential equation of all family of lines $y = mx + \frac{4}{m}$ by eliminating the arbitrary constant $m$ is

If $\frac{d y}{d t}+\alpha \cdot y=\gamma \cdot e^{-\beta t}$, then $\lim\limits_{t \to \infty } y\left( t \right)$ where $\alpha>0, \beta>0, \gamma>0, \alpha \neq \beta$, is equal to

A curve $y=f(x)$ is passing through $(0,0)$. If the slope of the curve at any point $(x, y)$ is equal to $(x+x y)$, then the number of solution of the equation $f(x)=1$, is:

The solution of the differential equation $\frac{{dy}}{{dx}} = {e^{3x - 2y}} + {x^2}{e^{ - 2y}}$, is

If $\frac{d y}{d x}=\frac{x+y-2}{x-y}$ and $y(0)=2$, find $y(2)$

Solution of the differential equation $y^2 d x+\left(x^2-x y+y^2\right) d y=0$ is

The solution of the differential equation $x^2 \frac{d y}{d x}=x^2+x y+y^2$ is

The general solution of the differential equation $\frac{{dy}}{{dx}} = \frac{{\left( {1 + {y^2}} \right)}}{{xy\left( {1 + {x^2}} \right)}}$ is

If $\frac{{dy}}{{dx}} = \frac{{xy}}{{{x^2} + {y^2}}},y\left( 1 \right) = 1$, then one of the values of ${x_0}$ satisfying $y\left( {{x_0}} \right) = e$ is given by

The solution of the differential equation $x \log x \frac{d y}{d x}+y=2 \log x$ is

The solution of the differential equation $(x+y)(d x-d y)=d x+d y$, is

The differential equation $\frac{d y}{d x}=\frac{\sqrt{1-y^2}}{y}$ determine of circles with

Let $y=y(x)$ be the solution of the differential equation $\left(x-x^3\right) d y=\left(y+y x^2-3 x^4\right) d x, x>2$. If $y(3)=3$, then $y(4)$ is equal to