What is the solution for (dy)/(dx)= x/(42+x^2) ?

The solution for (dy)/(dx)= x/(42+x^2) is y= 1/2 ln(42+x^2)+c_{1}

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(dy)/(dx)= x/(42+x^2)

\frac{d y}{d x} = \frac{x}{42 + x ^{2}}

y = \frac{1}{2} ln (42 + x^{2}) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{x}{42 + x ^{2}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{x}{42 + x ^{2}}

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

then

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

y = \int \frac{x}{42 + x ^{2}} d x

\int \frac{x}{42 + x ^{2}} d x = \frac{1}{2} ln (42 + x^{2}) + c_{1}

y = \frac{1}{2} ln (42 + x^{2}) + c_{1}

\int_{1}^{1000} \frac{1}{x ^{2}} d x

\int (y + 1) x^{2}

sin (π t)

y = 8 x, y = 8 x^{3}

\frac{d}{d x} (sin (y) + x y - x^{3})

What is the solution for (dy)/(dx)= x/(42+x^2) ?
The solution for (dy)/(dx)= x/(42+x^2) is y= 1/2 ln(42+x^2)+c_{1}