differential equations

**jones123** · January 9th 2013, 06:33 AM

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!

**GJA** · January 9th 2013, 07:29 AM

Hi jones123,

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

Does this clear things up? Good luck!

**adene364** · January 9th 2013, 11:41 PM

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