What is the solution for (dy)/(dx)=xe^y,y(0)=0 ?

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

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(dy)/(dx)=xe^y,y(0)=0

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

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

Solution steps

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

Solve separable ODE:

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

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

\int \frac{x ^{5} - x ^{3} + 1}{x ^{3} - x ^{2} - x + 1} d x

\int_{0}^{1} y^{4} d y

y = \frac{8}{4 + x ^{2}}, y = 1

\frac{\partial}{\partial x} (x^{4} - 4 x^{5} y)

x \to 0 lim (x^{4} cos (\frac{6}{x}))

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