Originally Posted by

**yen yen** when im doing questions that use integrating factors i always face the same problem.

eg.

dy/dx + P(x)y = Q(x)

and the integrating factor, I, would be e^(integral of P)

however after multiplying the whole equation by I, you would normally get something like

Iy' + IP(x)y = IQ(x)

and the next step would be combining the left hand side into (###)' so that you could equate ### to integral of the right hand side. what i want to ask is how do you get from Iy' + IP(x)y to first derivative of ###?

and example is

dx/dt + 4x/(100-t) = 3/2

im not sure if its correct but i got

P = 4/100-t

=> I = (100-t)^4 (correct this if im wrong)

then the equation becomes

x'(100-t)^4 + 4x(100-t)^3 = 3/2(100-t)^4

what do i do from here? i always get stuck at this step for all problems using integrating factors.