Solve Diff. Eq. Problem Using Substitution Method - Step by Step Guide

[scienceman2k9]

Problem:

y'=f(at+by+c) where a,b, and c are constants. Show that the substitution of x=at+by+c changes the equation to the separable equation x'=a+bf(x). Use this method to find the general solution of the equation y'=(y+t)^2


I really have no clue on this one. If someone could start me off in the right direction that would be great. I'm not seeing how they get that separable eq.

 

[xman]

Try writting the substitution as
$$x-at-c = by$$
Now take the derivative with respect to what I am assuming is the independent variable, t. The result should pop out at you.