What is the solution for (dy)/(dx)=(6ye^{3x})/(2+e^{3x)} ?

The solution for (dy)/(dx)=(6ye^{3x})/(2+e^{3x)} is y=4e^{c_{1}}+4e^{c_{1}+3x}+e^{c_{1}+6x}

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(dy)/(dx)=(6ye^{3x})/(2+e^{3x)}

\frac{d y}{d x} = \frac{6 y e ^{3 x}}{2 + e ^{3 x}}

y = 4 e^{c_{1}} + 4 e^{c_{1} + 3 x} + e^{c_{1} + 6 x}

Solution steps

\frac{d y}{d x} = \frac{6 y e ^{3 x}}{2 + e ^{3 x}}

Solve separable ODE:

y = 4 e^{c_{1}} + 4 e^{c_{1} + 3 x} + e^{c_{1} + 6 x}

y = 4 e^{c_{1}} + 4 e^{c_{1} + 3 x} + e^{c_{1} + 6 x}

\int_{- \infty}^{- 1} e^{- 28 t} d t

\frac{d}{d x} (x (x - 1)^{2} (x - 2)^{3})

\int π^{π} d x

y = x (3 x + 4)^{5}

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

What is the solution for (dy)/(dx)=(6ye^{3x})/(2+e^{3x)} ?
The solution for (dy)/(dx)=(6ye^{3x})/(2+e^{3x)} is y=4e^{c_{1}}+4e^{c_{1}+3x}+e^{c_{1}+6x}