# The general solution of the differential equation$$\frac{\large dy}{\large dx}=e^{x+y}$$is

$\begin{array}{1 1}(A)\;e^x+e^{-y}=C\qquad(B)\;e^x+e^y=C\\(C)\;e^{-x}+e^y=C\qquad(D)\;e^{-x}+e^{-y}=C\end{array}$

Toolbox:
• $e^{(x+y)}= e^x.e^y$
Step 1:
Given $\large\frac{dy}{dx}=$$e^{(x+y)} using the information in the tool box we get, \large\frac{dy}{dx}$$= e^x.e^y$
Now seperating the variables,