The solution to the Initial value problem
x′′+2x′+17x=2cos(6t),x(0)=0,x′(0)=0 is the sum of the steady
periodic solution xsp and the transient solution xtr. Find both xsp
and xtr.
Euler’s method
Consider the initial-value problem y′ = −2y, y(0) = 1. The
analytic solution is y(x) = e−2x . (a) Approximate y(0.1) using one
step of Euler’s method. (b) Find a bound for the local truncation
error in y1 . (c) Compare the error in y1 with your error bound.
(d) Approximate y(0.1) using two steps of Euler’s method. (e)
Verify that the global truncation error for Euler’s method is O(h)
by comparing the errors in parts (a) and...