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

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

\frac{d y}{d x} y = \frac{2 x}{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} y = \frac{2 x}{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}

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