Solve:

Find one-parameter families of solution curves of the following differential equations:

253.

Find one-parameter families of solution curves of the following differential equation:
 

Find one-parameter families of solution curves of the following differential equation:
 y'+3 y = e^mx (m: a given real number)

Find one-parameter families of solution curves of the following differential equation:
 y' - y = cos 2x

Find one-parameter families of solution curves of the following differential equation:
x y' - y = (x+1) e^-x

Find one-parameter families of solution curves of the following differential equation:
x y' + y = x⁴

Find one-parameter families of solution curves of the following differential equation:
x y' log x + y = log x

Find one-parameter families of solution curves of the following differential equation:

Find one-parameter families of solution curves of the following differential equation: