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  • Solve the differential equation frac{dy}{dx}+1=e^{x+y}

Solve the differential equation \frac{dy}{dx}+1=e^{x+y}

Answers (1)

\frac{dy}{dx}+1=e^{x+y}

To find: Solution of the given differential equation

Assume x+y=t

Differentiate on both sides with respect to x

1+\frac{dy}{dx}=\frac{dt}{dx}

Substitute

\frac{dy}{dx}+1=e^{x+y} in the above equation

e^{x+y}=\frac{dt}{dx}\\ e^{t}=\frac{dt}{dx}\\

Rewriting the equation,

dx=e^{-t}dt\\

Integrate on both the sides,

\int dx=\int e^{-t}dt\\ formula: \int e^{x}dx=e^{x}\\ x=-e^{-t}+c

Substituting \; t=x+y\\ x=-e^{-(x+y)}+c

Is the solution of the differential equation

Posted by

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