What is the solution for (dy)/(dx)=e^{x+y},y(0)=0 ?

The solution for (dy)/(dx)=e^{x+y},y(0)=0 is y=-ln(-e^x+2)

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(dy)/(dx)=e^{x+y},y(0)=0

\frac{d y}{d x} = e^{x + y}, y (0) = 0

y = - ln (- e^{x} + 2)

Solution steps

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

Solve separable ODE:

y = - ln (- e^{x} + 2)

y = - ln (- e^{x} + 2)

x (H (x) x)^{2} d x + x^{2} (H (x) x) (H (x) d x + x d H (x)) = 0

(x y^{2} - x) d x + (2 x^{2} y + 8 y) d y = 0

\frac{d}{d x} ((sin (π) x + cos (π) y)^{2}) = 2

y^{^{'}} = e^{- y} - 1

y^{^{'}} + y = 1, - H (t - 2) y (0) = 2

What is the solution for (dy)/(dx)=e^{x+y},y(0)=0 ?
The solution for (dy)/(dx)=e^{x+y},y(0)=0 is y=-ln(-e^x+2)