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Math Help - Differential Equation

  1. #1
    Junior Member
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    Differential Equation

    Need help with this guys....

    Solve the differential equation dy/dx = 4xy^2 and write the general solution in the form y^r + kx^n = C where r, k and n are numbers and C is the arbitary constant.

    Thanks...
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  2. #2
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    Aug 2008
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    (1/y^2)dy=4xdx

    integral of ((1/y^2)dy)= integral of (4xdx)

    -(1/y)+C1=2x^2+C2

    y= -(1/(2x^2))+C assume C2-C1=C

    y+(1/2)x^-2=C

    so r=1
    k=1/2
    n=-2
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  3. #3
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    Feb 2009
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    In this question maple has given me a different set of variables that doesnt work out so nicely.

    dy/dx = -5*x*y^4

    int(y^-4)dy = int (-5*x) dx

    1/3y^-3 - 5/2x^2 = C



    So when asked for the form y^r + kx^n = C, i have a 2nd constant before the y, namely 1/3, that is damaging to the answer. How could i have done this euation differently to avoid this error?
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