Reducing non-linear ODE to Linear

Hi all,

I'm struggling with the following problem.

Consider basic non linear differential equation:

dx/dt + a(t)x = b(t)x^{n}

I understand that I can define a new variable y = x^{1-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!

Re: Reducing non-linear ODE to Linear

Differentiate with respect to t so that or .

Sub it in along with the other bit then multiply through by 1-n and divide by x^n.

Re: Reducing non-linear ODE to Linear

Thank's it just clicked. Much appreciated :)