What is the solution for (6du)/(dt)=u^2 ?

The solution for (6du)/(dt)=u^2 is t=-6/u+c_{1}

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(6du)/(dt)=u^2

\frac{6 d u}{d t} = u^{2}

t = - \frac{6}{u} + c_{1}

Solution steps

\frac{6 d u}{d t} = u^{2}

Let

t

be the dependent variable. Divide by

d u

\frac{6}{\frac{d t}{d u}} = u^{2}

Substitute

\frac{d t}{d u}

with

t^{'} (u)

\frac{6}{t ^{^{'}} ( u )} = u^{2}

Isolate

t^{'} (u) : t^{'} (u) = \frac{6}{u ^{2}}

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

then

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

t = \int \frac{6}{u ^{2}} d u

\int \frac{6}{u ^{2}} d u = - \frac{6}{u} + c_{1}

t = - \frac{6}{u} + c_{1}

\frac{x ^{2} + 2 x}{4 x}

\frac{d y}{d x} = - y + 1

\int \frac{4 x - 3}{x} d x

y = ln (5 + 2 x + x^{3})

\int \frac{1}{cos ^{2} ( a y )} d y

What is the solution for (6du)/(dt)=u^2 ?
The solution for (6du)/(dt)=u^2 is t=-6/u+c_{1}