Ive been going through exam papers and theres a question on differential equations which I cant get to grips with

m*dv/dt = mg-kv [g> k/mv]

dv/dt= g-kv/m

∫dt =∫g-kv/m dv

im not sure on how to integrate this can anyone help explain it?

Printable View

- Nov 14th 2012, 02:07 AMVerdictGuiltyPast papers with brief solutions :(
Ive been going through exam papers and theres a question on differential equations which I cant get to grips with

m*dv/dt = mg-kv [g> k/mv]

dv/dt= g-kv/m

**∫***dt =*∫*g-kv/m dv*

im not sure on how to integrate this can anyone help explain it? - Nov 14th 2012, 02:38 AMMarkFLRe: Past papers with brief solutions :(
This is a linear ODE, and you want to write it in standard form:

Now, calculate the integrating factor and multiply the ODE by this:

Now, the left side is the differentiation of a product:

Can you proceed from here? - Nov 14th 2012, 02:40 AMa tutorRe: Past papers with brief solutions :(
Do you know how to use an Integrating factor - Wikipedia, the free encyclopedia?

- Nov 14th 2012, 02:47 AMmrmaaza123Re: Past papers with brief solutions :(
The integration for dt is simply "t".

The expression on the RHS is being integrated with respect to "v" so you should treat everything else as a constant and then proceed.

The expression ∫g-kv/m dv = g∫dv- k/m∫vdv

= gv- k/m(v^2/2)+c

Hope this helps. - Nov 14th 2012, 02:54 AMVerdictGuiltyRe: Past papers with brief solutions :(
hey thanks that helps alot guys I should be able to go from here thank you :)