(a) Suppose Y1(t) is a solution of an autonomous system dY/dt = F(Y). Show that Y2(t) = Y1(t +t0) is also a solution for any con
stant t0. (b) What is the relationship between the solution curves of Y1(t) and Y2(t)?
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Answer: 6 & 4.5 (m-per-h)
Step-by-step explanation:
- The basic formula used in this task is S=V*t, where S - distance, V - speed, t - time.
- the downstream speed is: V+Vc, where V - the speed of the boat in still water, Vc - the speed of the current.
- the upstream speed is: V-Vc.
- according to the described above the distance for downstream is S1=(V+Vc)*t1, where t1=10; the distance for upstream is S2=(V-Vc)*t2, where t2=70.
- for whole travel down- and upstream: S=S1+S2.
- Using these it is possible to make up the system of the equations:
V - the speed of the boat in still water - 6 miles per hour, Vc - the speed of the current - 4.5 miles per hour. All the details for the system of the equations are in the attachment.
