- #1

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## Homework Statement

How to integrate dv/dt=g-kv/m?

## Homework Equations

This is ODE.

## The Attempt at a Solution

dv/(g-(kv/m))=dt

Now what? I don't know how to integrate the left side.

- Thread starter Math10
- Start date

- #1

- 301

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How to integrate dv/dt=g-kv/m?

This is ODE.

dv/(g-(kv/m))=dt

Now what? I don't know how to integrate the left side.

- #2

Mark44

Mentor

- 34,687

- 6,394

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

How to integrate dv/dt=g-kv/m?

## Homework Equations

This is ODE.

## The Attempt at a Solution

dv/(g-(kv/m))=dt

Now what? I don't know how to integrate the left side.

- #3

- 301

- 0

What substitution?

- #4

- 301

- 0

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

- #5

- 301

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

- #6

Stephen Tashi

Science Advisor

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Are you saying you can't work [itex] \int {\frac{1}{g- \frac{kv}{m}} }dv [/itex] ?dv/(g-(kv/m))=dt

Now what? I don't know how to integrate the left side.

Could you do something like [itex] \int (3 -5v)^{-1} dv [/itex] ?

- #7

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

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