- #1

- 33

- 0

## Homework Statement

Multiply the given equation by the given integrating factor and solve the exact equation.

## Homework Equations

ydx+(2x-ye

^{y})dy=0, [tex]\mu[/tex](x,y)=y.

## The Attempt at a Solution

M=y

^{2}, N=2xy-y

^{2}e

^{y}

Integrating N=[tex]\Psi[/tex]

_{y}WRT x I get

xy

^{2}-((1/3)y

^{3}e

^{y}+ y

^{2}e

^{y})+h(x)=[tex]\Psi[/tex](x,y)

Differentiating [tex]\Psi[/tex](x,y) WRT x, I get

[tex]\Psi[/tex]

_{x}=y

^{2}+h'(x)

Thus h'(x)=0, and

[tex]\Psi[/tex](x,y)=xy

^{2}-((1/3)y

^{3}e

^{y}+ y

^{2}e

^{y})

The correct answer is xy

^{2}-(y

^{2}-2y+2)e

^{y}=c...

What am I doing wrong? When I solve for psi in the opposite way I get the same wrong answer from before...

Thanks in advance!