First order differential equation problem

**ViperRobK** · March 2nd 2009, 11:44 AM

I should really know the answer to this but am having trouble seeing it

I have a first order differential
$x\frac{dy}{dx} +\frac{y}{1-x} = (x-1)^2 sinx$
I get the intergrating factor $\frac{x}{1-x}$
but when multiplied through to get:
$\frac{x}{1-x}\frac{dy}{dx} + \frac{1}{(1-x)^2} y = (1-x) sinx$
i do not see the what the left side intergral should be any help would be greatly appreciated

**Krizalid** · March 2nd 2009, 11:49 AM

$\frac{x}{1-x}\cdot y'+\frac{y}{(1-x)^{2}}=\left( \frac{x}{1-x}\cdot y \right)'.$

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