Question

Help with separable equations?

Answer 1

y'tanx=a+y, y(Pi/3)=a 0<x<Pi/2

Answer 2

The answer given is:
\[y=\frac{ 4a }{ \sqrt{3} }sinx-a\]

Answer 3

let's try
\[\frac{dy}{dx}\tan(x)=a+y \\ \\ \frac{dy}{dx}=\frac{a+y}{\tan(x)} \\ \\ \frac{1}{a+y}\frac{dy}{dx}=\frac{1}{\tan(x)} \\ \\ \int\limits \frac{1}{a+y}dy=\int\limits\frac{1}{\tan(x)}dx\]

Answer 4

Can you continue from here?

Answer 5

Oh, I see what you did there. And yes I could, thank you