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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

\frac{d}{d x} (\frac{16}{x ^{2}})

\frac{\partial}{\partial y} (x y^{3} + x^{2})

\int \frac{2 + cos ( x )}{x} d x

\frac{d}{d j} (6 i + 8 j)

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