# How to integrate this?

1. Feb 3, 2015

### Math10

1. The problem statement, all variables and given/known data
How to integrate dv/dt=g-kv/m?

2. Relevant equations
This is ODE.

3. The attempt at a solution
dv/(g-(kv/m))=dt
Now what? I don't know how to integrate the left side.

2. Feb 3, 2015

### Staff: Mentor

The left side can be rewritten as $\frac{m \ dv}{mg - kv}$. There's a fairly obvious substitution you can use.

3. Feb 3, 2015

### Math10

What substitution?

4. Feb 3, 2015

### Math10

Never mind. I integrated and got (-m/k)ln abs(gm-kv)+C.

5. Feb 3, 2015

### Math10

Now, how to simplify (-m/k)ln abs(gm-kv)=t+C?

6. Feb 3, 2015

### Stephen Tashi

Are you saying you can't work $\int {\frac{1}{g- \frac{kv}{m}} }dv$ ?

Could you do something like $\int (3 -5v)^{-1} dv$ ?

7. Feb 3, 2015

### Math10

No, now I got it. I simplified and got gm-kv=Ce^(-kt/m).

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