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

The solution for (dy)/(dx)=(x^2)/(e^y) is y=ln((x^3)/3+c_{1})

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(dy)/(dx)=(x^2)/(e^y)

\frac{d y}{d x} = \frac{x ^{2}}{e ^{y}}

y = ln (\frac{x ^{3}}{3} + c_{1})

Solution steps

\frac{d y}{d x} = \frac{x ^{2}}{e ^{y}}

Solve separable ODE:

y = ln (\frac{x ^{3}}{3} + c_{1})

y = ln (\frac{x ^{3}}{3} + c_{1})

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x \frac{d y}{d x} - y = x

\frac{\partial}{\partial y} (y^{3} sin (4 x))

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\int x csch^{2} (\frac{x ^{2}}{2}) d x

What is the solution for (dy)/(dx)=(x^2)/(e^y) ?
The solution for (dy)/(dx)=(x^2)/(e^y) is y=ln((x^3)/3+c_{1})