What is the solution for (1+x^2)(dy)/(dx)-2xy=0 ?

The solution for (1+x^2)(dy)/(dx)-2xy=0 is y=e^{c_{1}}+e^{c_{1}}x^2

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(1+x^2)(dy)/(dx)-2xy=0

(1 + x^{2}) \frac{d y}{d x} - 2 x y = 0

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

Solution steps

(1 + x^{2}) \frac{d y}{d x} - 2 x y = 0

Solve separable ODE:

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

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

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

\frac{d}{d x} (x (ln (5 x))^{2})

\frac{d y}{d t} = (k (y - 60))

y^{^{'}} - 3 y = e^{3 x} 4 - x^{2}

x \to - 2 - lim (x + 1)

What is the solution for (1+x^2)(dy)/(dx)-2xy=0 ?
The solution for (1+x^2)(dy)/(dx)-2xy=0 is y=e^{c_{1}}+e^{c_{1}}x^2