Do you have to use the LT? I'm not sure of its effectiveness on a nonlinear equation like you have. On the other hand, your equation is Bernoulli. That's probably how I would attack it.
I am given the instructions "find a general solution to the equation"
given: y' + 2y = y^2 * e^x
i was able to take the laplace of the entire equation and what i got was
Sy(s) - y(0) + 2(y(s)) = 2 / (s-1)^3
the next part of this problem would be to plug in the givens and usually i would be given what y(0) equals to. how am i suppose to solve this transformation if i am unable to cancel out y(0)? was there something i was suppose to do to find the value of y(0)?
the answer i was provided is: y(e^x + Ce^2x) = 1; y = 0
this is on my practice final and any help would be much appreciated!