Differential Equations - General Solutions

Printable View

June 19th 2008, 12:02 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!
June 19th 2008, 12:05 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

$\sqrt[4]{\frac{4}{3}\cdot\frac{x^3}{3}+C_1}=|y|$
June 19th 2008, 12:13 PM
Nick87

Thanks, that helps alot! (Nod)

All times are GMT -8. The time now is 02:46 PM.

Copyright © 2005-2013 Math Help Forum. All rights reserved.

Copyright © 2005-2013 Math Help Forum. All rights reserved.