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

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

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y^'=(4xy)/(2+x^2)

y^{^{'}} = \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

y^{'} (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}

x \to - 4 lim (- x^{2} + 4 x - 9)

y^{^{''}} - 3 y^{^{'}} = t^{3} - 6

\int \frac{x ^{4}}{( 8 + x ^{5} ) ^{2}} d x

f (x) = ln (1 - x)

\int x^{2} x^{3} + 23 d x

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