What is the technique used to solve a separable differential equation?

Thread starter schattenjaeger
Start date Sep 12, 2005

AI Thread Summary

To solve the separable differential equation dy/dx = [x(y^2-2)]/(2x^2-6x+4), it can be rewritten as (xdx)/(2x^2-6x+4) = dy/(y^2-1). The left side can be simplified using partial fractions, while the right side may require a trigonometric substitution for integration. This method allows for easier integration of both sides. Proper application of these techniques is crucial to avoid errors in the solution process.

Sep 12, 2005

schattenjaeger

If you have the seperable DE...

dy/dx=[x(y^2-2)]/(2x^2-6x+4)

that eventually ends up

(xdx)/(2x^2-6x+4)=dy/(y^2-1), right

'cuz that's some integration I REALLY don't feel like doing by hand, so I don't want to do the wrong thing

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Sep 12, 2005

James R

Science Advisor

Homework Helper

Gold Member

That's

\frac{x}{2(x-2)(x-1)} dx= \frac{1}{y^2 -1}dy

Use partial fractions to do the left hand side, and a trig substitution on the right.

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