Find the general solution of the differential equation \frac{dy}{dx}= e^{x+y}.

 

 

 

 
 
 
 
 

Answers (1)

\frac{dy}{dx}= e^{x+y}
given  \frac{dy}{dx}= e^{x+y}
      \Rightarrow \frac{dy}{dx}= e^{x}.e^{y}\Rightarrow \frac{dy}{ey}= e^{x}.dx
     \Rightarrow e^{y}dy= e^{x}dx
on integration both side, we get
\int e^{-y}dy= \int e^{x}dx
\Rightarrow e^{-y}= e^{x}+c, which is the required solution.
 

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