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Please help me solve this differential equation: dy/dx-(1+1/x)y=y^2

  • Maths -

    This is just a special case of the Bernoulli Equation

    y' + p(x) y = q(x) y^n

    where q(x) = 1

    Make the substitution v = y^(1-n)
    This will give you

    -v' + (1+1/x)v = 1

    Now you can multiply by an integrating factor

    e^[∫(1+1/x) dx] = xe^x to get

    xe^x v = -e^x (x-1)

    and you're almost done

  • Maths -

    I'm not sure how to get the final answer

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