I need some help with this problem please:

solve by separation of variables.

dydx=y(1-y^2)

1/(y(1-y^2)dy=dx

How do I get it into y= form after taking the integral?

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- Feb 5th 2008, 05:44 PMyellowroseDifferential Equations-Separation of variables
I need some help with this problem please:

solve by separation of variables.

dydx=y(1-y^2)

1/(y(1-y^2)dy=dx

How do I get it into y= form after taking the integral? - Feb 5th 2008, 05:48 PMmr fantastic
- Feb 5th 2008, 06:01 PMyellowrose
- Feb 5th 2008, 06:20 PMJhevon
multiply through by $\displaystyle y(1 - y)(1 + y)$ to get $\displaystyle 1 = A(1 - y)(1 + y) + By(1 + y) + Cy(1 - y)$ .......(1)

then, plug in y = 0 into (1) and solve for A

then, plug in y = 1 into (1) and solve for B

then plug in y = -1 into (1) and solve for C - Feb 5th 2008, 06:34 PMKrizalid
$\displaystyle \frac{1}

{{y\left( {1 - y^2 } \right)}} = \frac{{\left( {1 - y^2 } \right) + y^2 }}

{{y\left( {1 - y^2 } \right)}} = \frac{1}

{y} + \frac{y}

{{1 - y^2 }}.$

Easily integrable.