Given the differential equation y’’ +5y’+6y=te^t with start
value y(0) = 0 and y’(0). Let Y(s) be the Laplace transformed of
y(t).
a) Find an expression for Y(s)
b) Find the solution to the equation by using inverse Laplace
transform.
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 ||