Consider the system modeled by the differential equation
dy/dt - y = t with initial condition y(0) = 1
the exact solution is given by y(t) = 2et − t − 1
Note, the differential equation dy/dt - y =t can be written as
dy/dt = t + y
using Euler’s approximation of dy/dt = (y(t + Dt) – y(t))/ Dt
(y(t + Dt) – y(t))/ Dt = (t + y)
y(t + Dt) =...
Initial value problem : Differential equations:
dx/dt = x + 2y
dy/dt = 2x + y
Initial conditions:
x(0) = 0
y(0) = 2
a) Find the solution to this initial value problem
(yes, I know, the text says that the solutions are
x(t)= e^3t - e^-t and y(x) = e^3t + e^-t
and but I want you to derive these solutions yourself using one
of the methods we studied in chapter 4) Work this part out on paper
to...