# Math Help - separable equation

1. ## separable equation

could someone please help me with this one? my answer doesn't match the one in the book so i know i'm doing something wrong but i'm not sure where.

$\frac{dy}{dx}=\sqrt{y}cos^2\sqrt{y}$

2. Originally Posted by yaykittyeee
could someone please help me with this one? my answer doesn't match the one in the book so i know i'm doing something wrong but i'm not sure where.

$\frac{dy}{dx}=\sqrt{y}cos^2\sqrt{y}$
If you post all your work then what you're doing wrong can be easily pointed out to you.

3. i start with the equation above, then i separated the dy/dx
$\frac{1}{\sqrt{y}cos^2\sqrt{y}}dy=dx$

then i integrate both sides and get
$2ln(cos^2\sqrt{y})=x+C$

that's as far as i get. i'm not sure that i'm integrating the left side right.

4. Originally Posted by yaykittyeee
$\frac{1}{\sqrt{y}cos^2\sqrt{y}}dy=dx$

then i integrate both sides and get
$2ln(cos^2\sqrt{y})=x+C$

that's as far as i get. i'm not sure that i'm integrating the left side right.
Your integration is wrong (differentiate it .... you don't get back the integrand). The correct approach would begin by making the substitution $u = \sqrt{y}$.