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

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

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

\frac{d y}{d x} y = e^{x + y}

y = - W (\frac{e ^{x} + c _{1}}{e}) - 1

Solution steps

\frac{d y}{d x} y = e^{x + y}

Solve separable ODE:

y = - W (\frac{e ^{x} + c _{1}}{e}) - 1

y = - W (\frac{e ^{x} + c _{1}}{e}) - 1

(x y + y^{2}) y^{^{'}} = x^{2} + x y, y (1) = 0

y^{^{'}} = x^{2} + y^{2} + x^{2} y^{2} + 1

a x^{^{'}} + b x = 0, x (0) = e^{r t}

(4 x^{5} - 16 x^{3} - 2 x) (1 - y^{2}) - 2 y (x^{2} - 4) y^{^{'}} = 0

\frac{d}{d x} (x^{2}) + \frac{d}{d x} (y^{2}) = 1

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