Separable differential equation question

find the solution of the differential equation that satisfies the given condition.

dy/dx = xysin(x)/(y+1) , y(0) = 1

dy/dx = xysin(x)/(y+1)

dy/dx = xsin(x)[y/(y+1)]

dy/[y/(y+1)] = xsin(x)dx

dy(1 + 1/y) = xsin(x)dx

now integrate both sides:

integral(xsin(x)dx) can be done with integration by parts
http://en.wikipedia.org/wiki/Integration…
u = x
v = -cosx

integral(xsin(x)dx) = -xcosx - integral(1 * -cosx)
=
-xcosx + sinx

y + ln(|y|) + C = -xcosx + sinx

now plug in initial values x = 0, y = 1 and find c

1 + ln(1) + C = 0 + 0

C = -1

y + ln(|y|) - 1 = -xcosx + sinx