What is the solution for (dy)/(dx)=(4xy)/(2+x^2) ?

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

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(dy)/(dx)=(4xy)/(2+x^2)

\frac{d y}{d x} = \frac{4 x y}{2 + x ^{2}}

y = 4 e^{c_{1}} + 4 e^{c_{1}} x^{2} + e^{c_{1}} x^{4}

Solution steps

\frac{d y}{d x} = \frac{4 x y}{2 + x ^{2}}

Solve separable ODE:

y = 4 e^{c_{1}} + 4 e^{c_{1}} x^{2} + e^{c_{1}} x^{4}

y = 4 e^{c_{1}} + 4 e^{c_{1}} x^{2} + e^{c_{1}} x^{4}

(1 + x)^{- \frac{4}{5}}

\frac{\partial}{\partial y} (e^{- \frac{y}{x}})

\frac{\partial}{\partial y} (x^{- 2} y^{- 3})

\frac{1}{2} x 25 - x^{2}

\int (\frac{3 x ^{3} - 4 x - 2}{x ^{3}}) d x

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