How do i obtain a function of V here: dv/dt +2V -9.8 = 0 i don't know which DE technique i should use
This is first-order linear ordinary differential equation:
Solve the separable equation ( dv(t))/( dt)+2V-9.8 = 0:
Solve for ( dv(t))/( dt):
( dv(t))/( dt) = -2.V+9.8
Integrate both sides with respect to t:
Answer: |v(t) = integral(-2.V+9.8) dt = (-2.V+9.8) t+c_1, where c_1 is an arbitrary constant
Though upper and lower case, I suspect that probably the two v's are intended to be the same, in which case, separating the variables,
\(\displaystyle \frac{dv}{dt}=9.8-2v\),
\(\displaystyle \frac{dv}{9.8-2v}=dt\),
\(\displaystyle \int\frac{1}{9.8-2v}dv=\int dt\),
etc..
Alternatively, you could write the equation as
\(\displaystyle \frac{dv}{dt}+2v=9.8\)
and use the integrating factor technique,
(multiply throughout by exp(2t)).
Tiggsy.
