I'm struggling with the following problem.
Consider basic non linear differential equation:
dx/dt + a(t)x = b(t)xn
I understand that I can define a new variable y = x1-n
However I am unsure how to make the general substituion to get to the solution:
dy/dt + (1-n)a(t)y = (1-n)b(t)
I would really appreciate it if someone could point me in the right direction and provide me with the steps.
I have tried differentiating it and substituting in for x dot but I still have x terms floating around.
Thank you for the help!