{a} write down two familiar functions that solve the equation (123:1!th = 9y. What is a solution y) that starts with y() = 3 and #10) = 0'? [h] Find [by hand] the eigenvalues A1 and A2 and corresponding eigenveotors 3:1 and 152 of 1 5 A' (1D 14)' {o} Consider the system of GDEs 5. = An: [note 2nd derivative!) with the A from part [b]. If mm = c1[t]a.'1 + 62(t)s:g, what equations do ct) and ct] satisfy, and hence what solutions ct) and ct] are possible? [See part {a}.} {d} For the DDE of part [oiI solve for 3\"] given the initial oonditions 3(0) = (2, 3) and :10) = (1,4). {e} Alternatively, if we let y be the 4-oomponent vector y = (3;, dzfr], then dyfr = By for B = . Since this must ultimately give the same solutions sit] as part to], what must be the eigenvalues of B