What is the solution for (dy)/(dx)=(x+1)/(e^y),y(0)=2 ?

The solution for (dy)/(dx)=(x+1)/(e^y),y(0)=2 is y=ln((x^2)/2+x+e^2)

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(dy)/(dx)=(x+1)/(e^y),y(0)=2

\frac{d y}{d x} = \frac{x + 1}{e ^{y}}, y (0) = 2

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = \frac{2}{3} x 1 - 9 y^{2}, y (0) = 0

(x + 1) y^{^{'}} - 3 y = 0

y^{^{'}} = 3 x^{2} y^{2}, y (- 1) = a, y (0) = 1

\frac{d y}{d x} = \frac{x y - 4 x + y - 4}{x y - 6 x - 3 y + 18}

\frac{d y}{d x} = x^{2} (y - 2), y (0) = 4

What is the solution for (dy)/(dx)=(x+1)/(e^y),y(0)=2 ?
The solution for (dy)/(dx)=(x+1)/(e^y),y(0)=2 is y=ln((x^2)/2+x+e^2)