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.
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!