# Reduction of differntial equation

1. May 2, 2014

### delsoo

1. The problem statement, all variables and given/known data

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...

2. Relevant equations

3. The attempt at a solution

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2. May 2, 2014

### SammyS

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

3. May 2, 2014

### delsoo

ln (V+1 ) as in my working

4. May 2, 2014

### LCKurtz

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

5. May 2, 2014

### delsoo

why cant i do in this way?

6. May 2, 2014

### LCKurtz

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

7. May 2, 2014

### SammyS

Staff Emeritus
Take the derivative of ln (V+1 ) .

It's 1/(V+1) .

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