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Math Help - Differential Equations (2)

  1. #1
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    Differential Equations (2)

    Solve the following differential equations using the substitution given.

    \displaystyle{\frac{dy}{dx}} + y = y^2, by substituting z = 1/y, given that y = 0.5 when x =0.

    Please guide me as to how to use the substitution....I'll try to figure out the rest on my own...Thank you!
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  2. #2
    Moo
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    Hi

    This time, I won't make any confusion

    z=\frac 1y \implies y=\frac 1z
    y(0)=0.5 \implies z(0)=2

    \frac{dy}{dx}=\frac{d(\tfrac 1z)}{dx}=-\frac{\tfrac{dz}{dx}}{z^2}=-\frac{dz}{dx} \frac 1{z^2}

    Substitute \frac{dy}{dx} and y in the DE and multiply by z^2
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