# Differential Equations - General Solutions

• Jun 19th 2008, 01:02 PM
Nick87
Differential Equations - General Solutions
Hey there, wondering if you could help me with a quick question please? :D

Okay this is the question:

1. Find the General Solution of the Equation:

$\frac{x^2}{y^3}$ $\frac{dx}{dy}$ = 3

Answer in the form $y=f(x)$

Any response muchly appreciated!
• Jun 19th 2008, 01:05 PM
Mathstud28
Quote:

Originally Posted by Nick87
Hey there, wondering if you could help me with a quick question please? :D

Okay this is the question:

1. Find the General Solution of the Equation:

$\frac{x^2}{y^3}$ $\frac{dx}{dy}$ = 3

Answer in the form $y=f(x)$

Any response muchly appreciated!

Multiplying both sides by $y^3dy$

Gives us

$x^2dx=3y^3dy$

Integrating both sides gives

$\frac{x^3}{3}+C=\frac{3y^4}{4}$

solving for y gives

$\sqrt[4]{\frac{4}{3}\cdot\frac{x^3}{3}+C_1}=|y|$
• Jun 19th 2008, 01:13 PM
Nick87
Thanks, that helps alot! (Nod)