# Math Help - Differential Equation

1. ## Differential Equation

Observe that is a solution, for any real c, of $y'=2ty$. Determine $c$ so that $y(0) = 2.$

Does anyone know how to solve this problem?Any help would be greatly appreciated, I'm pretty lost.

2. Originally Posted by cdlegendary
Observe that is a solution, for any real c, of $y'=2ty$. Determine $c$ so that $y(0) = 2.$

Does anyone know how to solve this problem?Any help would be greatly appreciated, I'm pretty lost.
Here you are being asked to find $c$ in $y=ce^{t^2}$ given the initial condition $y(0) = 2$

All you need to do is make $y=ce^{t^2}$ into $2=ce^{0^2}$ as per the initial condition.

Now solve $2=ce^{0^2}$ for $c$

$2=ce^{0^2}$

$2=ce^{0}$

$2=c\times 1$

$c = 2$