Solve the following differential equations:

$\frac{dy}{dx}-y=x{e}^x$

Solve the following differential equations 

$\frac{dy}{dx}+2y=x{e}^{4x}$

Solve the following differential equation :

$\frac{dy}{dx}+3y=e^{mx}, m$ is a given real number.

Solve the following differential equation:-

$\frac{dy}{dx}-y=\cos 2x$

Find one-parameter families of solution curves of the following differential equation.
(or Solve the following differential equations)

$x\frac{dy}{dx}-y=(x+1)e^{-x}$.

Find one-parameter families of solution curves of the following differential equation
(or Solve the following differential equation)

$x\frac{dy}{dx}+y=x^4$.

Find one-parameter families of solution curves of the following differential equation
(or Solve the following differential equation)

$\left(x\log x\right)\frac{dy}{dx}+y=\log x$

Solve the following differential equation :

$\frac{dy}{dx}-\frac{2xy}{1+x^2}=x^2+2$