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!
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!
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