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Math Help - another method of solving this ODE..

  1. #1
    Junior Member
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    another method of solving this ODE..

    another method of solving this ODE..
    (3x^2y-y^3)dx-(3xy^2-x^3)dy=0
    I ve proved that it is an exact differential equation ..
    I need to state another method with reasons of solving this ODE...

    Thanks..mate..whoever u are..
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  2. #2
    Junior Member roy_zhang's Avatar
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    Quote Originally Posted by ashes View Post
    another method of solving this ODE..
    (3x^2y-y^3)dx-(3xy^2-x^3)dy=0
    I ve proved that it is an exact differential equation ..
    I need to state another method with reasons of solving this ODE...

    Thanks..mate..whoever u are..
    I think you could try to divide both sides of the D.E. by x^3, this will transform the given D.E. into the form \left(3\left(\frac{y}{x}\right)-\left(\frac{y}{x}\right)^3\right)dx-\left(3\left(\frac{y}{x}\right)^2-1\right)dy=0
    then you can introduce a new dependent variable u(x)=\frac{y}{x} (or y=xu(x)), and express \frac{dy}{dx} in terms of x,\;u and \frac{du}{dx}. Now you have a separable D.E.

    Roy
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