What is the solution for y^'=(4xy)/(x^2+1) ?

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

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y^'=(4xy)/(x^2+1)

y^{^{'}} = \frac{4 x y}{x ^{2} + 1}

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

Solution steps

y^{'} (x) = \frac{4 x y}{x ^{2} + 1}

Solve separable ODE:

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

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

x y^{2} y^{^{'}} = x + x^{3}, y (1) = 2

\frac{d y}{d x} = \frac{1 + x}{y}

y^{^{'}} = \frac{sin ( x )}{y}, y (\frac{π}{2}) = 1

(1 - cos (x)) (\frac{d y}{d x}) = y sin (x)

y^{^{'}} (x) = \frac{4 + 3 x ^{2}}{3 y ^{2} - 12 y}, y (0) = 2

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