What is the solution for (dy)/(dx)=(5sqrt(x))/(e^y) ?

The solution for (dy)/(dx)=(5sqrt(x))/(e^y) is y=ln(10/3 x^{3/2}+c_{1})

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(dy)/(dx)=(5sqrt(x))/(e^y)

\frac{d y}{d x} = \frac{5 x}{e ^{y}}

y = ln (\frac{10}{3} x^{\frac{3}{2}} + c_{1})

Solution steps

\frac{d y}{d x} = \frac{5 x}{e ^{y}}

Solve separable ODE:

y = ln (\frac{10}{3} x^{\frac{3}{2}} + c_{1})

y = ln (\frac{10}{3} x^{\frac{3}{2}} + c_{1})

\frac{d v}{d t} = - 2 v

\frac{x ^{2} - 9}{x} \frac{d y}{d x} + y = 0

(x y + x) d x = (x^{2} y^{2} + x^{2} + y^{2} + 1) d y, y (1) = 2

\frac{d y}{d x} = - \frac{3}{7} x^{9} y^{8}

2 y^{^{'}} = y^{2} - 6 y + 9

What is the solution for (dy)/(dx)=(5sqrt(x))/(e^y) ?
The solution for (dy)/(dx)=(5sqrt(x))/(e^y) is y=ln(10/3 x^{3/2}+c_{1})