Observe that is a solution, for any real c, of $\displaystyle y'=2ty$. Determine $\displaystyle c$ so that $\displaystyle y(0) = 2.$
Does anyone know how to solve this problem?Any help would be greatly appreciated, I'm pretty lost.
Observe that is a solution, for any real c, of $\displaystyle y'=2ty$. Determine $\displaystyle c$ so that $\displaystyle y(0) = 2.$
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 $\displaystyle c$ in $\displaystyle y=ce^{t^2}$ given the initial condition $\displaystyle y(0) = 2$
All you need to do is make $\displaystyle y=ce^{t^2}$ into $\displaystyle 2=ce^{0^2}$ as per the initial condition.
Now solve $\displaystyle 2=ce^{0^2}$ for $\displaystyle c$
$\displaystyle 2=ce^{0^2}$
$\displaystyle 2=ce^{0}$
$\displaystyle 2=c\times 1$
$\displaystyle c = 2$