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Math Help - Plz help me

  1. #1
    IzI
    IzI is offline
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    Plz help me

    Please solve this problem and guide me. thanks in advance
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  2. #2
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    Re: Plz help me

    To do this you need to make the substitution \displaystyle \begin{align*} z = y^{-1} \end{align*}. Then \displaystyle \begin{align*} y = z^{-1} \implies \frac{dy}{dx} = -z^{-2}\,\frac{dz}{dx} \end{align*}. Then your DE becomes

    \displaystyle \begin{align*} \frac{dy}{dx} + x\,y &= x\,y^2 \\ -z^{-2}\,\frac{dz}{dx} + x\, z^{-1} &= x\,z^{-2} \\ \frac{dz}{dx} - x\,z &= -x  \end{align*}

    which is now linear.
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