If $\frac{dy}{dx} = 2xy$ and $y = 3$ when $x = 0$, what is $y$ when $x = 1$?

Explanation

1. 01

   Separating and integrating gives the general solution; the condition $y(0) = 3$ fixes the constant.

2. 02

   The particular solution is $y = 3 e^{x^{2}}$.

3. 03

   At $x = 1$: $y = 3 e$.