So in this problem we are given that

(xlnx)y' + y = x^2 * e^x

and

y(e) = 1

I under stand how it needs to be solved (need to get all y on one side, all x on other side, then integrate, then solve for y, then sub in y(e) = 1 to determine value of C.

I can only get this far, however:

dy/dx = (x^2 * e^x)/xlnx + y/xlnx

I could factor out the 1/xlnx, but it wouldn't be separable. I could do some minor simplifying, but then it wouldn't be factorable.

Any help is greatly appreciated