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Math Help - bernoulli problem

  1. #1
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    bernoulli problem

     y'=y+xy^{3}

    need some help!
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  2. #2
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    Krizalid's Avatar
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    \begin{aligned}<br />
   y'&=y+xy^{3} \\ <br />
  y'-y&=xy^{3} \\ <br />
  \frac{y'}{y^{3}}-\frac{1}{y^{2}}&=x.<br />
\end{aligned}

    Make the substitution z=\frac1{y^2}.
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by skystar View Post
     y'=y+xy^{3}

    need some help!
    Read the section Bernoulli's Equations in my Differential Equations Tutorial. This may help you out a bit...

    Make the substitution v=y^{-2} \implies y=v^{-\frac{1}{2}} to make it linear.
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