Question

solve the following ordinary differential equations.
*dv/dt=9.8-v/5
*dp/dt=0.5p-450
*dm/dt=500-0.4m

Answer 1

By separation of variables...\[\frac{ dv }{ dt} = 9.8 - \frac{ v }{ 5 } = \frac{ 1 }{ 5 }(49 - v)\]
\[\frac{ dv }{ (49 - v) } = \frac{ 1 }{ 5 }dt\]
Now integrate both sides

Answer 2

The others can be solved in a similar way:
\[\frac{ dp }{ dt}=0.5p-450 = 0.5(p-900)\]
\[\frac{ dm }{ dt }=0.4( 1250-m)\]

Answer 3

thank you!

Answer 4

No prob.