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Math Help - differential equation

  1. #1
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    differential equation

    can anyone help me with this
    Find the general solution of x.dy/dx-y=x^2.e^x
    thanks for any help
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  2. #2
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    Quote Originally Posted by hmmmm View Post
    can anyone help me with this
    Find the general solution of x.dy/dx-y=x^2.e^x
    thanks for any help
    Put in standard form

    (1)\;\;\;\frac{dy}{dx} - \frac{y}{x} = x e^x

    The integrating factor is \mu = exp(\int -\frac{1}{x}\,dx) = \frac{1}{x}. Multiplying (1) by this gives

    \frac{1}{x} \left( \frac{dy}{dx} - \frac{y}{x} \right) = \frac{d}{dx} \left( \frac{1}{x} \cdot y \right) = e^x

    If you let u = \frac{y}{x} your equation will separate.
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