What is the solution for (7du)/(dt)=u^2 ?

The solution for (7du)/(dt)=u^2 is t=-7/u+c_{1}

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(7du)/(dt)=u^2

\frac{7 d u}{d t} = u^{2}

t = - \frac{7}{u} + c_{1}

Solution steps

\frac{7 d u}{d t} = u^{2}

Let

t

be the dependent variable. Divide by

d u

\frac{7}{\frac{d t}{d u}} = u^{2}

Substitute

\frac{d t}{d u}

with

t^{'} (u)

\frac{7}{t ^{^{'}} ( u )} = u^{2}

Isolate

t^{'} (u) : t^{'} (u) = \frac{7}{u ^{2}}

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

then

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

t = \int \frac{7}{u ^{2}} d u

\int \frac{7}{u ^{2}} d u = - \frac{7}{u} + c_{1}

t = - \frac{7}{u} + c_{1}

4 y^{^{''}} + 8 y = 0

\int_{- 1}^{1} x^{\frac{1}{3}} d x

x \to - 1 lim (sin (π x))

x \to 0 + lim ((tan (3 x))^{x})

y = e^{5 x}, y = e^{6 x}, x = 1

What is the solution for (7du)/(dt)=u^2 ?
The solution for (7du)/(dt)=u^2 is t=-7/u+c_{1}