Answer to Question #232788 in Differential Equations for Nika

Question

(e^2x + 4) dy/dx = y

Answer 1

$\frac{dx}{e^{2x}+4}=\frac{dy}{y}$

$Let z=e^{2x}+4$

$dz=2e^{2x}dx=2(z-4)dx$

$dx=\frac{dz}{2(z-4)}$

$\frac{dy}{y}=\frac{dx}{z}=\frac{dz}{2z(z-4)}=1/8(\frac{1}{z-4}-\frac{1}{z})dz$

$lny=1/8(ln(z-4)-lnz)+C$

$lny=1/8(2x-ln(e^{2x}+4))+C$