What is the solution for derivative of sqrt(v)= 1/(2sqrt(v)) ?

The solution for derivative of sqrt(v)= 1/(2sqrt(v)) is v(x)=x+c_{1}

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derivative of sqrt(v)= 1/(2sqrt(v))

\frac{d}{d x} (v) = \frac{1}{2 v}

v (x) = x + c_{1}

Solution steps

\frac{d}{d x} (v (x)) = \frac{1}{2 v ( x )}

Simplify

(v (x))^{'} = \frac{1}{2 v ( x )} : \frac{v ^{'} ( x )}{2 v ( x )} = \frac{1}{2 v ( x )}

Isolate

v^{'} (x) : v^{'} (x) = 1

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

then

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

v (x) = \int 1 d x

\int 1 d x = x + c_{1}

v (x) = x + c_{1}

\int (4 - x) 8^{(4 - x)^{2}} d x

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{'}} - x e^{y} = 2 e^{y}

\frac{d y}{d x} + 5 y = 3

\int \frac{3 x - 4}{x ^{2} - 3 x + 2} d x

What is the solution for derivative of sqrt(v)= 1/(2sqrt(v)) ?
The solution for derivative of sqrt(v)= 1/(2sqrt(v)) is v(x)=x+c_{1}