Question

Help me solve this differential equation for v(t)!

Answer 1

\[\dfrac{dv}{dt}+bm_0e^{-\gamma t}v+(g-u\gamma)=0\]b, m_0, γ, g, and u are constants (γ is probably negative, with the other ones positive).

Answer 2

take \((g-u\gamma)\) to the right hand side

find an integrating factor \(R(t)=e^{\int bm_0e^{-\gamma t} \text dt}\)

\[\frac{\text{d}}{\text d t}\left(R(t)v\right)=R(t)(g-u\gamma)\]

Answer 3

you dont have to include the constant of integration in the integrating factor, you'll get one later down the line.