Question1: For the system of differential equations below:
x'=-x+y x(0)=3
y'=-24x+9y y(0)=14
Find the particular solution for the given IC: x(0)=3, y(0)=14. Write the answer x(t),y(t)
Question 2: On the interval t=[0, L] solve the end point problem: x''+9x=1 with BC x(0)=x(L)=0.
Hint use Fourier method.
Question3: Solve x''+9x=s(t-4) using Laplace transform. IC: x(0)=x'(0)=0.