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Thread: [SOLVED] Find DE given slope and point?

  1. #1
    Senior Member mollymcf2009's Avatar
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    [SOLVED] Find DE given slope and point?

    Find the equation of the curve that passes thru the point (0,1) & whose slope at (x,y) is 13xy.

    I'm not sure how to start this. Can someone get me started without doing the whole prob?
    Thanks
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  2. #2
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    skeeter's Avatar
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    \frac{dy}{dx} = 13xy

    separate variables ...

    \frac{dy}{y} = 13x \, dx

    integrate ...

    \ln|y| = \frac{13x^2}{2} + C_1

    y = C_2e^{\frac{13x^2}{2}}

    y(0) = 1

    1 = C_2e^0

    C_2 = 1

    y = e^{\frac{13x^2}{2}}
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