Methods of Solving First Order, First Degree Differential Equation

Solution of the following differential equation

$\frac{dy}{dx}=x\sqrt{25-x^2}$ is

The solution of the following differential equation $y-x\frac{dy}{dx}=0$ is

Solve the differential equation $(x+2y)(dx-dy)=dx+dy$.

General solution of the differential equation $\left(x+2\right)\frac{dy}{dx}=x^2+4x-9$ is

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

Solution of $\frac{dy}{dx}=e^{y+x}+e^y{x}^2$ is :

Solution of $\frac{dy}{dx}={\cos }^2\left(y\right)$ is:

Solution of $\frac{dy}{dx}+\frac{1}{y}+y=0$ is:

Solution of $e^{-x+y}\frac{dy}{dx}=1$ is:

Solution of $\frac{dy}{dx}=\frac{e^x+e^{-x}}{e^x-e^{-x}}$ is:

Solution of $\frac{dy}{dx}+\cos x\tan y=0$ is:

Solution of $\frac{dy}{dx}+2x=e^{3x}$ is

Solution of differential equation $\left(x^2+1\right)\frac{dy}{dx}=1$ is :

The particular solution of $\frac{dy}{dx}+1=e^{x+y}$ at $(0, 0)$ is

Which one of the following is a homogeneous differential equation.

The integrating factor of the differential equation $x\frac{dy}{dx}-y=x^2$ is

The solution of the differential equation $\frac{dy}{dx}+xy={xy}^2$ is: (where $c$ is an arbitrary constant)

If $x\left(1+y^2\right)dx+y\left(1+x^2\right)dy=0$ and $y\left(0\right)=1,$ then $x^2{y}^2+x^2+y^2$ is equal to

When $y=vx,y$ and $x$ are variables, the differential equation $\frac{dy}{dx}=\frac{2xy}{x^2-y^2}$ reduces to

Integrating factor of the differential equation $\left(1+x^2\right)dy+2xy dx=\cot x dx, x\ne 0$ is