Posted by **Robert** on Monday, August 6, 2012 at 8:20pm.

Solve the differential equation dy/dx = -xe^y and determine the equation of the curve through P(1,2)

I tried solving the differential equation and I get y = log(x^2/2 + C).

Is this correct?

Now I forgot how to find the equation.

Thank you!

- Calculus -
**MathMate**, Monday, August 6, 2012 at 8:59pm
Your solution is almost good, just a change of the sign will fix it.

y=-log(x^2/2+C)

If it has to pass through P(1,2)

substitute x=1, and y=2 and find C.

2=-log(1/2+C)

log(1/2+C)=-2

take logs

1/2+C=e^(-2)

C=e^(-2)-1/2

so

y=-log(x²/2+e^(-2)-1/2)

- Calculus -
**Paul**, Monday, August 6, 2012 at 9:14pm
thanks a lot mate

- Calculus -
**Robert**, Monday, August 6, 2012 at 9:22pm
oops, that was under my brother's name hehe

- Calculus :) -
**MathMate**, Tuesday, August 7, 2012 at 7:39am
You're both welcome!

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