Question

Find the solution to the following differential equation. dv/dt =9.8-0.196v

Answer 1

\[\frac{dv}{dt}=9.8-0.196v\]\[\frac{dv}{dt}+0.196v=9.8\]\[v=v_h+v_p\]\[v_h=C\exp{(-0.196t)}\quad,\quad v_p=\frac{9.8}{0.196}=50\]\[v=C\exp{(-0.196t)}+50\]