Question

For the differential equation in) pin -1) + ... + Polly with solutions ....Yo Abel's formula for the Wronskian is Wy ... (t) = cel ot Consider the equation (4) - y 0 . (a) Use Abel's formula from above to find the Wronskian of a fundamental set of solutions of the given equation. (Use as the constant mentioned in Abel's formula.) w(t) ce el cost, and sint. (b) Determine the Wronskian of the solutions d Wel, e, cost, sin t) - 8 (c) Determine the Wronkian of the solutions cosh, sinhcost, and sint. Wicosht, sinh t, cost, sint)

Answer 1

@ Consider the given aquation y( y no. where as is a constant W(t)a celodtte, where 6 wlet, et arst, sind) let let - Let et tat 1cest sint a t reint est et arst sink 1 et sint ast et ast -sint - et sink aust S 1 1 Sint -art I I I al 2 2 1 -2 ast asing o 0 sich I cast Ra=Rztri O RARAAR 0 ast Sinta 1-) -sirt ask Ri=RATR3 0 4 0 0 0 li ast sinky = (-4). Li - sing at 2(-4) (2) - sint ast racollast sint

@ w/ lisht, sicht, cast, Sint) - lacht saht, cost sont suht Cosht esinf cost asht sinhit list sont sicht asht but both - 1 asht sicht, best sint te sinht lacht -sint ast R12h3-R, lo O -20st - 2 sint RRARO o öll ziet uzast you Cashrt - Sinert) (aart + 4 sort)? - 14() - 4.