What is the solution for (dy)/(dx)=(3x)/(3+x^2) ?

The solution for (dy)/(dx)=(3x)/(3+x^2) is y= 3/2 ln(3+x^2)+c_{1}

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(dy)/(dx)=(3x)/(3+x^2)

\frac{d y}{d x} = \frac{3 x}{3 + x ^{2}}

y = \frac{3}{2} ln (3 + x^{2}) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{3 x}{3 + x ^{2}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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

y = \int \frac{3 x}{3 + x ^{2}} d x

\int \frac{3 x}{3 + x ^{2}} d x = \frac{3}{2} ln (3 + x^{2}) + c_{1}

y = \frac{3}{2} ln (3 + x^{2}) + c_{1}

y^{^{'}} + x \cdot e^{- x^{\frac{2}{2}}} = 0

\int (x - 1) cos (\frac{x}{3}) d x

\frac{d}{d x} (x^{0.2})

e^{6 s i n (7 x)}

\frac{d}{d x} (\frac{π}{3})

What is the solution for (dy)/(dx)=(3x)/(3+x^2) ?
The solution for (dy)/(dx)=(3x)/(3+x^2) is y= 3/2 ln(3+x^2)+c_{1}