Find the solution of $\frac{d y}{d x}=2^{y-x}$.

Find the differential equation of all non-vertical lines in a plane.

If $\frac{d y}{d x}=e^{-2 y}$ and $y=0$ when $x=5$, then find the value of $x$ when $y=3$.

Solve $\left(x^2-1\right) \frac{d y}{d x}+2 x y=\frac{1}{x^2-1}$.

Solve $\frac{d y}{d x}+2 x y=y.$

Find the general solution of $\frac{d y}{d x}+a y=e^{m x}$.

Solve the differential equation $\frac{d y}{d x}+1=e^{x+y}$.

Solve $y d x-x d y=x^2 y d x$.

Solve the differential equation $\frac{d y}{d x}=1+x+y^2+x y^2$, when $y=0$ and $x=0$.

Find the general solution of $\left(x+2 y^3\right) \frac{d y}{d x}=y$.

If $y(x)$ is a solution of $\left(\frac{2+\sin x}{1+y}\right) \frac{d y}{d x}=-\cos x$ and $y(0)=1$, then find the value of $y\left(\frac{\pi}{2}\right)$.

If $y(t)$ is a solution of $(1+t) \frac{d y}{d t}-t y=1$ and $y(0)=-1$, then show that $y(1)=-\frac{1}{2}$.

Form the differential equation having $y=\left(\sin ^{-1} x\right)^2+A \cos ^{-1} x+B$, where $A$ and $B$ are arbitrary constants, as its general solution.

Form the differential equation of all circles which pass through origin and whose centres lie on $Y$-axis.

Find the equation of a curve passing through origin and satisfying the differential equation $\left(1+x^2\right) \frac{d y}{d x}+2 x y=4 x^2$.

Solve $x^2 \frac{d y}{d x}=x^2+x y+y^2$.

Find the general solution of the differential equation $\left(1+y^2\right)+\left(x-e^{\tan ^{-1} y}\right) \frac{d y}{d x}=0$

Find the general solution of $y^2 d x+\left(x^2-x y+y^2\right) d y=0$.

Solve $(x+y)(d x-d y)=d x+d y$.

Solve $2(y+3)-x y \frac{d y}{d x}=0$, given that $y(1)=-2$.

Solve the differential equation $d y=\cos x(2-y \operatorname{cosec} x) d x$ given that $y=2$, when $x=\frac{\pi}{2}$.

Form the differential equation by eliminating $A$ and $B$ in $$A x^2+B y^2=1$$

Solve the differential equation $\left(1+y^2\right) \tan ^{-1} x d x+2 y\left(1+x^2\right) d y=0$.

Find the differential equation of system of concentric circles with centre $(1,2)$.

Solve $y+\frac{d}{d x}(x y)=x(\sin x+\log x)$.

Find the general solution of $(1+\tan y)(d x-d y)+2 x d y=0$.

Solve $\frac{d y}{d x}=\cos (x+y)+\sin (x+y)$.

Find the general solution of $\frac{d y}{d x}-3 y=\sin 2 x$.

Find the equation of a curve passing through $(2,1)$, if the slope of the tangent to the curve at any point $(x, y)$ is $\frac{x^2+y^2}{2 x y}$.

Find the equation of the curve through the point $(1,0)$, if the slope of the tangent to the curve at any point $(x, y)$ is $\frac{y-1}{x^2+x}$.

Find the equation of a curve passing through origin, if the slope of the tangent to the curve at any point $(x, y)$ is equal to the square of the difference of the abcissa and ordinate of the point.

Find the equation of a curve passing through the point $(1,1)$, if the tangent drawn at any point $P(x, y)$ on the curve meets the coordinate axes at $A$ and $B$ such that $P$ is the mid-point of $A B$.

Solve $x \frac{d y}{d x}=y(\log y-\log x+1)$

The degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^2=x \sin \left(\frac{d y}{d x}\right)$ is

The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^{3 / 2}=\frac{d^2 y}{d x^2}$ is

The order and degree of the differential equation $\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^{1 / 4}+x^{1 / 5}=0$ respectively, are

If $y=e^{-x}(A \cos x+B \sin x)$, then $y$ is a solution of

The differential equation for $y=A \cos \alpha x+B \sin \alpha x$, where $A$ and $B$ are arbitrary constants is

The solution of differential equation $x d y-y d x=0$ represents

The integrating factor of differential equation $\cos x \frac{d y}{d x}+y \sin x=1$ is

The solution of differential equation $\tan y \sec ^2 x d x+\tan x \sec ^2 y d y=0$ is

The family $y=A x+A^3$ of curves is represented by differential equation of degree

The integrating factor of $\frac{x d y}{d x}-y=x^4-3 x$ is

The solution of $\frac{d y}{d x}-y=1, y(0)=1$ is given by

The number of solutions of $\frac{d y}{d x}=\frac{y+1}{x-1}$, when $y(1)=2$ is

Which of the following is a second order differential equation?

The integrating factor of differential equation $\left(1-x^2\right) \frac{d y}{d x}-x y=1$ is

$\tan ^{-1} x+\tan ^{-1} y=C$ is general solution of the differential equation

The general solution of $e^x \cos y d x-e^x \sin y d y=0$ is

The degree of differential equation $\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3+6 y^5=0$ is

The solution of $\frac{d y}{d x}+y=e^{-x}, y(0)=0$ is

The integrating factor of differential equation $\frac{d y}{d x}+y \tan x-\sec x=0$ is

The solution of differential equation $\frac{d y}{d x}=\frac{1+y^2}{1+x^2}$ is

The integrating factor of differential equation $\frac{d y}{d x}+y=\frac{1+y}{x}$ is

$y=a e^{m x}+b e^{-m x}$ satisfies which of the following differential equation?

The solution of differential equation $\cos x \sin y d x+\sin x \cos y d y=0$ is

The solution of $x \frac{d y}{d x}+y=e^x$ is

The differential equation of the family of curves $x^2+y^2-2 a y=0$, where $a$ is arbitrary constant, is

The family $Y=A x+A^3$ of curves will correspond to a differential equation of order

The general solution of $\frac{d y}{d x}=2 x e^{x^2-y}$ is

The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is

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

The solution of equation $(2 y-1) d x-(2 x+3) d y=0$ is

The differential equation for which $y=a \cos x+b \sin x$ is a solution, is

The solution of $\frac{d y}{d x}+y=e^{-x}, y(0)=0$ is

The order and degree of differential equation

$$\left(\frac{d^3 y}{d x^3}\right)^2-3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^4 \text { are }$$

The order and degree of differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]=\frac{d^2 y}{d x^2}$ are

The differential equation of family of curves $y^2=4 a(x+a)$ is

Which of the following is the general solution of $\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}+y=0$ ?

The general solution of $\frac{d y}{d x}+y \tan x=\sec x$ is

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

The general solution of differential equation $\left(e^x+1\right) y d y=(y+1) e^x d x$ is

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

The solution of differential equation $\frac{d y}{d x}+\frac{2 x y}{1+x^2}=\frac{1}{\left(1+x^2\right)^2}$ is

The degree of the differential equation $\frac{d^2 y}{d x^2}+e^{d y / d x}=0$ is ............ .

The degree of the differential equation $\sqrt{1+\left(\frac{d y}{d x}\right)^2}=x$ is ................. .

The number of arbitrary constants in the general solution of a differential equation of order three is .......... .

$\frac{d y}{d x}+\frac{y}{x \log x}=\frac{1}{x}$ is an equation of the type ........... .

General solution of the differential equation of the type is given by ............ .

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

The solution of $\left(1+x^2\right) \frac{d y}{d x}+2 x y-4 x^2=0$ is .............. .

The solution of the differential equation $y d x+(x+x y) d y=0$ is ............ .

General solution of $\frac{d y}{d x}+y=\sin x$ is ............ .

The solution of differential equation $\cot y dx=xdy$ is ............ .

The integrating factor of $\frac{d y}{d x}+y=\frac{1+y}{x}$ is ............. .

Integrating factor of the differential of the form $\frac{d x}{d y}+P_1 x=Q_1$ is given by $e^{\int P_1 d y}$.

Solution of the differential equation of the type $\frac{d x}{d y}+P_1 x=Q_1$ is given by $x \cdot \mathrm{IF}=\int(\mathrm{IF}) \times Q_1 d y$.

Correct substitution for the solution of the differential equation of the type $\frac{d y}{d x}=f(x, y)$, where $f(x, y)$ is a homogeneous function of zero degree is $y=v x$.

Correct substitution for the solution of the differential equation of the type $\frac{d y}{d x}=g(x, y)$, where $g(x, y)$ is a homogeneous function of the degree zero is $x=v y$.

Number of arbitrary constants in the particular solution of $a$ differential equation of order two is two.

The differential equation representing the family of circles $x^2+(y-a)^2=a^2$ will be of order two.

The solution of $\frac{d y}{d x}=\left(\frac{y}{x}\right)^{1 / 3}$ is $y^{2 / 3}-x^{2 / 3}=c$

Differential equation representing the family of curves $y=e^x(A \cos x+B \sin x)$ is $\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}+2 y=0$

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

Solution of $\frac{x d y}{d x}=y+x \tan \frac{y}{x}$ is $\sin \left(\frac{y}{x}\right)=c x$

The differential equation of all non horizontal lines in a plane is $\frac{d^2 x}{d y^2}=0$