# differential equations homework urgent!

• December 23rd 2008, 01:27 AM
GabrielKiefer
differential equations homework urgent!
Solve the homogenous differential equation (x^2 – xy + y^2)dx + x^2dy = 0 by completing the steps below
a. define a new variable in terms of the existing variables. State the resulting differential equation
b. using part a, substitute into the given differential equation. Then simplify. Show your work.
c. Integrate the resulting equation. Show your work
d. Using the definition from part a, rewrite your answer in terms of the original variables. Show your work.
• December 23rd 2008, 03:33 PM
Krizalid
$\frac{dy}{dx}=-\frac{x^{2}-xy+y^{2}}{x^{2}}.$

Divide top & bottom by $x^2$ and then put $y=xz.$ (This seems to be pure homework, I hope you can do something by your own.)