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

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

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

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

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

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

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

\int \frac{x}{x ^{2} + 1} d x = \frac{1}{2} ln (x^{2} + 1) + c_{1}

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

2 x y^{^{'}} + y = 6 x, y (4) = 14

\int 2 y + 2 d y

\int \frac{sin ( 4 x )}{cos ( 4 x )} d x

f (x) = \frac{x ^{2}}{x - 5}

\frac{1}{s ( s + 1 ) ( s + 2 )}

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