Now applying the substitution , we see that the DE becomes
Now separating the variables, we have
Now we integrate. The LHS becomes .
Now we need to do some manipulation on the RHS.
Note that . Now when we integrate wrt u, we have .
So it turns out that we have .
Backsubstituting , we have
Continuing with the simplification, we have
My solution and the books solution disagree...due to one variable...XD
Are you sure you copied it down correctly?