What is the solution for (dy)/(dx)=1+e^{y-x+3} ?

The solution for (dy)/(dx)=1+e^{y-x+3} is y=-ln(-x-c_{1})+x-3

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(dy)/(dx)=1+e^{y-x+3}

\frac{d y}{d x} = 1 + e^{y - x + 3}

y = - ln (- x - c_{1}) + x - 3

Solution steps

\frac{d y}{d x} = 1 + e^{y - x + 3}

Solve using substitution:

y = - ln (- x - c_{1}) + x - 3

y = - ln (- x - c_{1}) + x - 3

\int (\frac{x + 8}{x}) d x

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What is the solution for (dy)/(dx)=1+e^{y-x+3} ?
The solution for (dy)/(dx)=1+e^{y-x+3} is y=-ln(-x-c_{1})+x-3