What is the solution for (dy)/(dx)=(16sqrt(x))/(e^y) ?

The solution for (dy)/(dx)=(16sqrt(x))/(e^y) is y=ln(32/3 x^{3/2}+c_{1})

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(dy)/(dx)=(16sqrt(x))/(e^y)

\frac{d y}{d x} = \frac{16 x}{e ^{y}}

y = ln (\frac{32}{3} x^{\frac{3}{2}} + c_{1})

Solution steps

\frac{d y}{d x} = \frac{16 x}{e ^{y}}

Solve separable ODE:

y = ln (\frac{32}{3} x^{\frac{3}{2}} + c_{1})

y = ln (\frac{32}{3} x^{\frac{3}{2}} + c_{1})

y^{^{''}} + 4 y = 12 sin (2 x)

f (x) = \frac{4}{3 x ^{2}} + \frac{1}{x ^{2.1}}

\int \frac{( 8 + x + x ^{2} )}{x} d x

x \to 4 - lim (\frac{6 x}{x - 4})

f (x) = 3 sin^{2} (x)

What is the solution for (dy)/(dx)=(16sqrt(x))/(e^y) ?
The solution for (dy)/(dx)=(16sqrt(x))/(e^y) is y=ln(32/3 x^{3/2}+c_{1})