What is the solution for (dy)/(dx)=(2xy)/(1+x^2) ?

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

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(dy)/(dx)=(2xy)/(1+x^2)

\frac{d y}{d x} = \frac{2 x y}{1 + x ^{2}}

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

Solution steps

\frac{d y}{d x} = \frac{2 x y}{1 + x ^{2}}

Solve separable ODE:

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

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

g (x) = 7 x, at x = 9

\frac{d y}{d t} = 1600 - \frac{4 y}{170}

\frac{\partial}{\partial x} (\frac{x ^{2} y - 1}{x ^{2}})

\frac{d}{d x} (21 x)

\frac{\partial}{\partial x} (20 - x^{2} - 7 y^{2})

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