State University of New York Ordinary Differential Equation Questions

answer the following question and show the work neatly and understandable!

notes attached

1.(30 points) Find the solutions of X’ = AX with
A=
1 0 1
1 1 1
-1 0 3
(Hint: section 7.4]
2. (30 points) Solve the initial value problem
x” – 3x’ + 2x = e sint – text, #(0) = 0, x'(0) = 0
(Hint: section 5.4 or section 5.6 or section 11.4]
3. (40 points) Find the first six coefficients 20, …, as of the power series
solution x(t) = [nao ant” of the initial value problem
x” + ta’ – e’x = 0,
x(0) = 1, x'(0) = 2.
(Hint: make use of the Taylor series of et = [no )
at I lost
RO
Odont