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Calculus

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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 -

    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 -

    thanks a lot mate

  • Calculus -

    oops, that was under my brother's name hehe

  • Calculus :) -

    You're both welcome!

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