# Math Help - Differential Equations - General Solutions

1. ## Differential Equations - General Solutions

Hey there, wondering if you could help me with a quick question please?

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!

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

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

$\sqrt[4]{\frac{4}{3}\cdot\frac{x^3}{3}+C_1}=|y|$

3. Thanks, that helps alot!