[Math] Finding solution to a differential equation given the initial condition

Question

Given $dy/dx = 2y/(2x+1)$ and the initial condition $y(0)=e$ and $x>-1/2$, find the solution y.

I was able to separate the variables and integrate both sides respectively. I then tried to use the initial condition to find my Constant of integration but I get lost after that step. I don't know how i am supposed to isolate y from $ln(2y)$ on the left side of the equation.

Answer 1

${{dy}\over y}={{2dx}\over{2x+1}}$ implies that $ln(|y|)=ln(|2x+1|)+c$, you deduce that $y=A(2x+1)$ and $A=e$.