Question

Consider the vectors х() 3 (, 1)T х°() — (?, 26)Т. and i) Compute the Wronskian of X1 and X2 at t ii) In what intervals are X1 and X2 linearly independent? iii What conclusion can be drawn about the coefficients in the systems of homogeneous differential equation satisfied by X1 and X2? v) Find this system of equations and verify the conclusions of part iii

Answer 1

olotion and 2t)e t at)7 t2 x 1'te)at) wronneion o k2t) i w (ce), t)) t t 2 :f th t) k2t) au nealy 6now ar Ce independent mean to te (-,0) (0, 0) at and 2, (t) t2 ct+d o, at tb kon attt sbt at ct+atd hna fom

Roloiny dleve eaton on we alt ao, 6, c 1 doe not erist af t o ave C kd ct) Clhes