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solve the following differential equation: (x^2+xy)dy=(xy-y^2)dx

  • university maths -

    See if this works:
    http://www.math.colostate.edu/~gerhard/M345/CHP/ch2_6.pdf

    It does not look like it meets the "exact differential" requirements

  • university maths -

    Good reference. Try looking at the last example:

    Substitute y = xv ⇒ dy = v dx+x dv

    (xy-y^2)dx - (x^2+xy)dy = 0
    (x^2v - x^2v^2)dx - (x^2 + x^2v)(vdx + xdv) = 0

    2/x dx + (1+v)/v^2 dv = 0

    2lnx + (lnv - 1/v) = C

    ln(x^2v) - 1.v = C

    vx^2 = Cexp(1/v)
    y = vx

    xy = Cex/y

    Check my math, as always.

  • university math -

    I want to congratulate and thank Steve for that very impressive solution.

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