What is the solution for (dy)/(dx)= x/(x^2+4) ?

The solution for (dy)/(dx)= x/(x^2+4) is y= 1/2 ln(x^2+4)+c_{1}

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(dy)/(dx)= x/(x^2+4)

\frac{d y}{d x} = \frac{x}{x ^{2} + 4}

y = \frac{1}{2} ln (x^{2} + 4) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{x}{x ^{2} + 4}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{x}{x ^{2} + 4}

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

then

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

y = \int \frac{x}{x ^{2} + 4} d x

\int \frac{x}{x ^{2} + 4} d x = \frac{1}{2} ln (x^{2} + 4) + c_{1}

y = \frac{1}{2} ln (x^{2} + 4) + c_{1}

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What is the solution for (dy)/(dx)= x/(x^2+4) ?
The solution for (dy)/(dx)= x/(x^2+4) is y= 1/2 ln(x^2+4)+c_{1}