First, divide the equation through by x to get

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

Hmm...

My solution and the books solution disagree...due to one variable...XD

Are you sure you copied it down correctly?