What is the solution for (ds}{\frac{dt)/2}=sqrt(s) ?

The solution for (ds}{\frac{dt)/2}=sqrt(s) is t=4sqrt(s)+c_{1}

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(ds}{\frac{dt)/2}=sqrt(s)

\frac{d s}{\frac{d t}{2}} = s

t = 4 s + c_{1}

Solution steps

\frac{d s}{\frac{d t}{2}} = s

Let

t

be the dependent variable. Divide by

d s

\frac{1}{\frac{\frac{d t}{d s}}{2}} = s

Substitute

\frac{d t}{d s}

with

t^{'} (s)

\frac{1}{\frac{t ^{^{'}} ( s )}{2}} = s

Isolate

t^{'} (s) : t^{'} (s) = \frac{2}{s}

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

then

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

t = \int \frac{2}{s} d s

\int \frac{2}{s} d s = 4 s + c_{1}

t = 4 s + c_{1}

\frac{d ^{10}}{d x ^{10}} (cos (2 x))

t^{2} \cdot \frac{d x}{d t} = \frac{1}{x}

\frac{d}{d x} (8 x e^{4 x})

\int \frac{sin ^{2} ( x )}{x ^{2}} d x

f (x) = \frac{e ^{x}}{1 - e ^{x}}

What is the solution for (ds}{\frac{dt)/2}=sqrt(s) ?
The solution for (ds}{\frac{dt)/2}=sqrt(s) is t=4sqrt(s)+c_{1}