I'm having troubles solving this question:

Given: 2tx(dx/dt) = 4t² + 3x²

Rewrite this equation for y(t) = x(t)² and then solve it.

I'd probably know how to solve it, but i don't know how to rerwrite it!

Thanks!

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- Jan 9th 2013, 06:33 AMjones123differential equations
I'm having troubles solving this question:

Given: 2tx(dx/dt) = 4t² + 3x²

Rewrite this equation for y(t) = x(t)² and then solve it.

I'd probably know how to solve it, but i don't know how to rerwrite it!

Thanks! - Jan 9th 2013, 07:29 AMGJARe: differential equations
Hi jones123,

If $\displaystyle y(t)=x(t)^{2},$ then the chain rule says $\displaystyle \frac{dy}{dt}=2x\frac{dx}{dt}.$ So $\displaystyle \frac{1}{2x}\frac{dy}{dt}=\frac{dx}{dt}.$ Now use this and $\displaystyle y=x^{2}$ to make substitutions in the orginal DE and try to solve the new equation for $\displaystyle y(t).$

Does this clear things up? Good luck! - Jan 9th 2013, 11:41 PMadene364AVS College
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