# Math Help - Differential equation

1. ## Differential equation

I am currently studying differential equations and stumbled upon this problem:

$\frac{dy}{dx} = \frac{3x^2}{2y + cos(y)}, y(0) = pi$

Any help is much appreciated,

Dranalion

2. It's a separation of variables. Basically cross multiply and integrate.

3. I have solved to here:

$(2y + cos(y))dy = (3x^2)dx$

$\int (2y + cos(y))dy = \int (3x^2)dx$

$y^2 + sin(y) = x^3 + c$

How do I get y by itself (as a function of x)

4. Originally Posted by Dranalion
I have solved to here:

$(2y + cos(y))dy = (3x^2)dx$

$\int (2y + cos(y))dy = \int (3x^2)dx$

$y^2 + sin(y) = x^3 + c$

How do I get y by itself (as a function of x)
You can't.

The best you can do is get an explicit function $x(y)$.

$x = \sqrt[3]{y^2 + \sin{y} + C}$.

Now use your initial condition to find $C$.