a.) Suppose

y′1=t^2y1+4y2+sec(t)

y′2=sin(t)y1+ty2−6.

This system of linear differential equations can be put in the form y'=P(t)y+g(t).

Determine P(t) and g(t)

b.) Suppose

(t+3)y′1=5ty1+9y2

(t−6)y′2=9y1+4ty2 y1(1)=0, y2(1)=2

This system of linear differential equations can be put in the form y'=P(t)y+g(t).

Determine P(t) and g(t)

Find the largest interval a

c.) Two solutions of a 2×2 first order linear system are given by

y1=[e^(5t),e^(5t)], y2=[−e^(−t) ,2e^(−t)]

Set up the Wronskian of the two solution

Wronskian = det