This problem can be solved as in...

http://www.mathhelpforum.com/math-he...tml#post510114

Setting for semplicity sake the DE becomes...

(1)

Now because is...

(2)

... we obtain from (1)...

(3)

... i.e. a separable variables DE the solution of which is...

(4)

... just like in Your textbook. The further step could be finding ... a little less confortable step ...

Kind regards