Differential equation

**Dranalion** · October 22nd 2009, 03:58 AM

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

**BobP** · October 22nd 2009, 04:38 AM

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

**Dranalion** · October 24th 2009, 12:14 AM

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)

**Prove It** · October 24th 2009, 12:27 AM

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 $C$ .

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