What is the solution for (du+2dv)/(u+2v)=0 ?

The solution for (du+2dv)/(u+2v)=0 is v=-1/2 u+c_{1}

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(du+2dv)/(u+2v)=0

\frac{d u + 2 d v}{u + 2 v} = 0

v = - \frac{1}{2} u + c_{1}

Solution steps

\frac{d u + 2 d v}{u + 2 v} = 0

Let

v

be the dependent variable. Divide by

d u

\frac{1 + 2 \cdot \frac{d v}{d u}}{u + 2 v} = 0

Substitute

\frac{d v}{d u}

with

v^{'} (u)

\frac{1 + 2 v ^{^{'}} ( u )}{u + 2 v} = 0

Isolate

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

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

then

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

v = \int - \frac{1}{2} d u

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

v = - \frac{1}{2} u + c_{1}

x \to 2 lim (3 x^{2} - 2 x + 1)

f (x) = \frac{7 x ^{2} + 7 x + 7}{x}

y = (x^{(3)} - 4 x)^{(12)} (2)

\frac{\partial}{\partial y} (y + cos^{2} (x))

\int \frac{1}{x ^{2} - 6 x} d x

What is the solution for (du+2dv)/(u+2v)=0 ?
The solution for (du+2dv)/(u+2v)=0 is v=-1/2 u+c_{1}