Having problems solving this diff equation.

(1-x^2)y´+ xy = x for -1 < x < 1

I get the ínt factor to 1/(1-x^2)^0,5, But having problems after that.

Thank you.

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- Mar 16th 2008, 10:04 AM #1

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- Mar 16th 2008, 10:29 AM #2

- Mar 16th 2008, 10:34 AM #3

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- Mar 16th 2008, 10:36 AM #4

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- Mar 16th 2008, 10:39 AM #5
ok, so following the steps exactly, you would end up with

$\displaystyle \frac 1{\sqrt{1 - x^2}}y' + \frac x{(1 - x^2)^{3/2}}y = \frac x{(1 - x^2)^{3/2}}$

again, just following the steps i outlined (we literally don't have to think about this if we know the steps by heart), this becomes

$\displaystyle \left( \frac 1{\sqrt{1 - x^2}}y\right)' = \frac x{(1 - x^2)^{3/2}}$

now integrate both sides and continue

look closely at the steps and see what is confusing you. the single derivative is simply the coefficient of y' times y.

- Mar 16th 2008, 10:42 AM #6

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- Mar 16th 2008, 10:43 AM #7

- Mar 16th 2008, 10:46 AM #8

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