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Math Help - General Solution to a Differential Equation

  1. #1
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    General Solution to a Differential Equation

    Find the general solution to x^2y' + y^2(x^2+1)=0.
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  2. #2
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    Separable

    This is a first order nonlinear differential equation, so there will be one arbitrary constant in the solution, and we cannot use the standard methods that we would for a linear equation. However, this one is separable:
    x^2 y' + y^2 (x^2 + 1) = 0
    x^2 y' = -y^2 (x^2 + 1)

    \dfrac{1}{y^2}\dfrac{dy}{dx} = -\dfrac{x^2 + 1}{x^2}

    \dfrac{dy}{y^2} = -(1+\dfrac{1}{x^2})dx

    From here you can integrate, and solve the result for y to get the general equation.

    --Kevin C.
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