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h Bessel equation of order p is ty" + ty + (t? - p2 y =...


h Bessel equation of order p is ty + ty + (t? - p2 y = 0. In this problem assume that p= 2. a) Show that y1 = sint/Vt and y2
(o if 0 <t < 12, y(t) = { 2 if 12 < t < 15, 0 if 15 <t
h Bessel equation of order p is ty" + ty + (t? - p2 y = 0. In this problem assume that p= 2. a) Show that y1 = sint/Vt and y2 = cost/vt are linearly independent solutions for 0 <t<o. b) Use the result from part (a), and the preamble in Exercise 3, to find the general solution of ty" + ty' + (t2 - 1/4)y = 3/2 cost.
(o if 0 <t < 12, y(t) = { 2 if 12 < t < 15, 0 if 15 <t
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of order p is Given Bessel equation ry + ty + (4² p² y = 0 Putting P = ty + ty + ( 12 4 )y=0 V Vt Y2 = Cost for old coo. (aon How satisfying values of Y s Lits of eq. O, we get 1.His = 2 1 2 1 5/2 cast + 312 hint - tv2 eart) + + 1 - 2 + 1 cast -(b) using result from general solution of part (as to find the ty +ty + (+24) 4 = 1312 Cost from part (as it is proved thatMow U2 = ( y.gt). I W(Y,Z) sint. est - dt → 42 = -) sint (ast at > U2 = -f Sin (24) at 2 sint Gst- &in (24) 4 cs(24) How putt

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