What is the solution for (dy)/(dx)=(x^2)/(6e^y) ?

The solution for (dy)/(dx)=(x^2)/(6e^y) is y=ln((x^3)/(18)+c_{1})

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(dy)/(dx)=(x^2)/(6e^y)

\frac{d y}{d x} = \frac{x ^{2}}{6 e ^{y}}

y = ln (\frac{x ^{3}}{18} + c_{1})

Solution steps

\frac{d y}{d x} = \frac{x ^{2}}{6 e ^{y}}

Solve separable ODE:

y = ln (\frac{x ^{3}}{18} + c_{1})

y = ln (\frac{x ^{3}}{18} + c_{1})

f (x) = 4 x^{2} - 7 x

3 t sin (t)

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

x y^{^{'}} - 3 y^{2} = 0

3 e^{- 7 t} cos (\frac{t}{3} + \frac{π}{3})

What is the solution for (dy)/(dx)=(x^2)/(6e^y) ?
The solution for (dy)/(dx)=(x^2)/(6e^y) is y=ln((x^3)/(18)+c_{1})