First Order ODE

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• February 7th 2011, 03:04 PM
robotENGR
First Order ODE
I am trying to solve:

$(2*-x*\frac{dy}{dx}) +(\frac{dy}{dx})-{y(x)}-1=0$

and I seem to be missing a step: when I solve this i get y = 1 which doesn't seem right.

Thank you for your help
• February 7th 2011, 03:10 PM
pickslides
This can be re-written as $\displaystyle \frac{dy}{dx}(1-2x)=y+1$ which is separable.

It becomes $\displaystyle \frac{dy}{y+1}= \frac{dx}{1-2x}$
• February 7th 2011, 03:40 PM
Prove It
It's also first order linear if written as

$\displaystyle \frac{dy}{dx} + \frac{1}{2x - 1}\,y = -\frac{1}{2x-1}$

and so you can use the Integrating Factor Method...