Solve the differential equation Y’(t) = AY(t), with initial
condition Y(0) = [1;0] (a 2x1 matrix); where A = [ 9 , 5 ; -6 , -2
]. Then, using Euler’s method with step size h=.1 over [ 0 , .5 ]
fill in the table with header where the 2x1 matrix Yi is the
approximation of the exact solution Y(ti) :
t Yi Y(ti) ||Y(ti) – Yi ||
Take the Laplace transform of the following initial value and
solve for Y(s)=L{y(t)}: y′′+4y={sin(πt) ,0, 0≤t<11≤t
y(0)=0,y′(0)=0
Y(s)= ? Hint: write the right hand side in
terms of the Heaviside function. Now find the inverse transform to
find y(t). Use step(t-c) for the Heaviside function u(t−c) .
y(t)= ?