Question

(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of 2 parts correctly. Consider the differential equation: 9ty' - 2t(t +9)y +2(t+9) y = -26, t>0. You can verify that yı = 3t and y2 = 2texp(2t/9) satisfy the corresponding homogeneous equation. a. Compute the Wronskian W between yı and 32- W(t) = b. Apply variation of parameters to find a particular solution. Bre,+2te (*),+22

Answer 1

method of variation of parameters - Consider the differential equation a y"+ P(A) y tady = f(t) Assume that y, (t) and fact) are a fundamental set of solutions for hongereais equation - 9"+ Pd) 24 Ә) 9 = 0 Then a particular solution to the man dengacars libberental equation et a Yplt) = 4,9, + UgGq where you uict) = 1 G P (t) at :) WCY1G2) and utt) = (y, Rett et WyY) where, WCY, G) is Wraskida a Girena gstry" at eft9)y'+ 2 H+9)y=-gt² sto on yll - 3 (1+27)y't 9 ( 1 + 1) = -2 t Heren Plt) = -2/3 (179) = -2 -2 / OCH = CH+9) and Ret)= 2 bircha y = 3st and Yg = get exp (24/0) can wets - 14, )= Wet) = lyg yg | late eta eto 24 24 34. = 3 t. 21 19 12 + t2 t) - bet 21 I 3

Wit) = 34 e 49 (+44-2) = 3:4 ** eitto peptie wat Howa (ad esto (st) at 4 t eating = Sets dt = 1 and Ught) = ( 3t. (- at det 2. ext/5 =-S* etio det = -t [ 22419] - / Hercea Ypest) = 4,9, +" Gg YpC+= (3+ gest/9 (24 estra) [Yped) = A2+18t. Ans