- #1

aaronfue

- 122

- 0

## Homework Statement

Given: (x

^{2}-y

^{2})dx + (x

^{2}-xy)dy=0,

Verify that the following function is a solution for the given differential equation:

c

_{1}(x+y)

^{2}=xe

^{y/x}

**2. The attempt at a solution**

I've gotten this far:

1st - I solved for [itex]\frac{dy}{dx}[/itex] in the given equation.

[itex]\frac{dy}{dx}[/itex]=[itex]\frac{-x^2-y^2}{x^2-xy}[/itex]

2nd - I used implicit differentiation on the function and got:

2c

_{1}(x+y)(1+y)=xe

^{y/x}([itex]\frac{xy'-y}{x}[/itex]) + e

^{y/x}

Now...I believe that I can solve for y' in: 2c

_{1}(x+y)(1+y)=xe

^{y/x}([itex]\frac{xy'-y}{x}[/itex]) + e

^{y/x}?