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

The solution for (dy)/(dx)=(2x)/(y(1+x^2)) is y=sqrt(2ln(1+x^2)+c_{1)},y=-sqrt(2ln(1+x^2)+c_{1)}

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

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

y = 2 ln (1 + x^{2}) + c_{1}, y = - 2 ln (1 + x^{2}) + c_{1}

Solution steps

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

Solve separable ODE:

y = 2 ln (1 + x^{2}) + c_{1}, y = - 2 ln (1 + x^{2}) + c_{1}

y = 2 ln (1 + x^{2}) + c_{1}, y = - 2 ln (1 + x^{2}) + c_{1}

f (x) = ln ((x - 1) (x + 1)^{2})

\int_{1}^{x^{3}} t^{2} d t

x \to 0 lim (\frac{e ^{- 5 x} - 1}{x})

\frac{d}{d x} (cos (5 x^{2} - x))

f (x) = 2 x^{2} + 3 x, at x = - 2

What is the solution for (dy)/(dx)=(2x)/(y(1+x^2)) ?
The solution for (dy)/(dx)=(2x)/(y(1+x^2)) is y=sqrt(2ln(1+x^2)+c_{1)},y=-sqrt(2ln(1+x^2)+c_{1)}