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