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

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

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

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

y = \frac{1}{( x ^{2} + 1 ) ( ln ( x ^{2} + 1 ) + c _{1} )}

Solution steps

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

Solve Bernoulli ODE:

y = \frac{1}{( x ^{2} + 1 ) ( ln ( x ^{2} + 1 ) + c _{1} )}

y = \frac{1}{( x ^{2} + 1 ) ( ln ( x ^{2} + 1 ) + c _{1} )}

\int_{1}^{x} 2 (x - 1) d x

f (x) = arctan (x^{10})

3 t^{4} + 7 t^{2} - 5

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