# Math Help - Nonlinear ODE

1. ## Nonlinear ODE

$y' = 4t^2y^2$

Hint: write the ODE as (F(y))' = G(t).

I don't understand how to use the hint. I understand that I need to combine y' and y^2 into the form (F(y))'; I just don't know how.

I only got to $\frac{y'}{y^2} = 4t^2$

Thanks!

2. $\displaystyle \frac{dy}{dt} = 4t^2y^2$

$\displaystyle y^{-2}\,\frac{dy}{dt} = 4t^2$

$\displaystyle \int{y^{-2}\,\frac{dy}{dt}\,dt} = \int{4t^2\,dt}$

$\displaystyle \int{y^{-2}\,dy} = \int{4t^2\,dt}$.

Go from here.

3. Originally Posted by Truthbetold
$y' = 4t^2y^2$

Hint: write the ODE as (F(y))' = G(t).

I don't understand how to use the hint. I understand that I need to combine y' and y^2 into the form (F(y))'; I just don't know how.

I only got to $\frac{y'}{y^2} = 4t^2$

Thanks!
Notice that $\dfrac{y'}{y^2} = - \dfrac{d}{dt} \left( \dfrac{1}{y}\right).$