1. ## IVP

If we use separation of variables to try to solve the IVP

we would obtain a solution that could not be put in explicit form. But we can solve for $\displaystyle y^2$ instead -- do this.

How would I go about solving for $\displaystyle y^2$? So far I've only had problems where I've had to solve for $\displaystyle y$, and I'm not sure what to do here.

2. Originally Posted by cdlegendary
If we use separation of variables to try to solve the IVP

we would obtain a solution that could not be put in explicit form. But we can solve for $\displaystyle y^2$ instead -- do this.

How would I go about solving for $\displaystyle y^2$? So far I've only had problems where I've had to solve for $\displaystyle y$, and I'm not sure what to do here.
$\displaystyle \frac{dy}{dt}=\frac{t^2}{y}$

$\displaystyle y\ dy = t^2\ dt$

Integrate both sides: $\displaystyle \int y\ dy = \int t^2\ dt$

$\displaystyle \frac{y^2}{2} + K_1 = \frac{t^3}{3} + K_2$

$\displaystyle y^2 = \frac{2t^3}{3} + C$

And that's solved for $\displaystyle y^2$

Hope that helped

Mathemagister