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

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

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

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

y = ln (\frac{2}{3} x^{\frac{3}{2}} + c_{1})

Solution steps

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

Solve separable ODE:

y = ln (\frac{2}{3} x^{\frac{3}{2}} + c_{1})

y = ln (\frac{2}{3} x^{\frac{3}{2}} + c_{1})

3 x^{2} - 2

f (x) = - 9.8 x^{2} + 2 x + 1

\int \frac{1}{arcsin ( x ) 1 - x ^{2}} d x

\frac{\partial}{\partial x} (x^{2} + x y + y^{2} + 2 x - y)

\frac{d}{d t} (- cos (2 t))

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