Let x(t) x₁ (t) x' (t) x₁ (t): = = If x (0) = x₂(t): = = = ] Put the eigenvalues in ascending order when you enter x₁ (t), x₂(t) below. exp( t) + exp( x₁(t) x₂(t) -27 x₁(t) + 12x₂(t) -56 x₁(t) + 25 x₂(t) 4 be a solution to the system of differential equations: -2 exp( find x(t). t) + exp( t) t)

П Write the function f(x) = x (1-x) as an eigenfunction ex- pansion of the eigenfunctions corresponding to the Sturm-Liouville prob- lem y" + Xy = 0, 0 < x < y(0) = 0 y (H) = 0 πT

x'(t) = of the any - 2 5-6 4 1-4-6|x (t) x (0) = -2 + -3 1 The only eigen value of this matrix is -3, a triple root. You must explicitly find matrix involved, with the exception cannot involve Also, your answer 0 imaginary any matrix inverses. number i.

Given that A = (14) has eigenvalues -1 and 3 with 3-eigenvector equal to [H] 2 -1 A = ^-636369* and -1-eigenvector equal to 2 , fill in the blank: