Question

The solution of $\frac{dy}{dx}+1=e^{x+y}$ is

• A. $e^{-(x+y)}+x+c=0$
• B. $e^{-(x+y)}-x+c=0$
• C. $e^{x+y}+x+c=0$
• D. $e^{x+y}-x+c=0$

Answer 1

The correct option is A $e^{-(x+y)}+x+c=0$

$x+y=z\Rightarrow 1+\frac{dy}{dx}=\frac{dz}{dx}\frac{dy}{dx}+1=e^{x+y}\Rightarrow \frac{dy}{dx}=e^{-z}dz=dx\Rightarrow \int e^{-z}dz=\int dx\Rightarrow -e^{-z}=x+c\Rightarrow e^{-(x+y)}+x+c=0.$