Please help!!!!

Question

From below choices, select the correct general solution for the following Separable ODE:

A.) ,   is an arbitrary constant.

B.),    is an arbitrary constant.

C.),     is an arbitrary  constant.

D.),  C is an arbitrary constant.

Answer 1

y' = e^{3x + y};dy/dx = e^3x·e^y; e^{- y}dy = e^3xdx; ∫ e^{- y}dy = ∫e^3xdx; - e^{- y}+ C = 1/3e^3x; 1/e^y = C - 1/3e^3x;

e^y = 1/(C - 1/3e^3x); y = ln[1/(C- 1/3e^3x)]; C is arbitrary constant.

So right answer is C.)