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

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

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

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

y = 2 1 + x^{2} + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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

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

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

y = 2 1 + x^{2} + c_{1}

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