1. Calculus issue

How to solve this problem?

dy/dx= 2y, y(1)= 3

2. Originally Posted by Abalo
How to solve this problem?

dy/dx= 2y, y(1)= 3
This is a first order seperable ODE so

$\frac{dy}{dx}=2y \iff \frac{dy}{y}=2dx$

Now just integrate both sides to get

$\ln|y|=2x+C \iff y=e^{2x+c}\iff y=Ae^{2x}$

Now just use the inital condition to solve for A.