Reduction of differntial equation

[delsoo]

Homework Statement

for this question, i 'm only able reduce it to become x dv/dx = (v^2 + 1) / v ... i have checked it several times, i just couldn't find my mistake...

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

for this question, i 'm only able reduce it to become x dv/dx = (v^2 + 1) / v ... i have checked it several times, i just couldn't find my mistake...

Homework Equations

The Attempt at a Solution

What is \displaystyle \ \int\frac{v}{v^2+1}\,dv\ ?

 

[delsoo]

ln (V+1 ) as in my working

 

[LCKurtz]

ln (V+1 ) as in my working

$$\frac v {v^2+1} \ne \frac v {v(v+1)}$$

 

[delsoo]

why can't i do in this way?

 

[LCKurtz]

Because you can't make up your own algebra rules.$$
\frac v {v(v+1)}= \frac v {v^2+v} \ne \frac v {v^2+1}$$

 

[SammyS]

What is \displaystyle \ \int\frac{v}{v^2+1}\,dv\ ?

ln (V+1 ) as in my working

Take the derivative of ln (V+1 ) .

It's 1/(V+1) .


To do that integration, the substitution, u =(v²+1) works very nicely .