Question

Solve the non-homogeneous differential equation duce = {}; 5] uc) + [26] with initial condition u(0) = ).

Answer 1

4,0 -0 General E17-6(-1)+34 solutionai uz(t) a uski +4 (0) = et (cocoast tcasin 5t) - 5 ais 34, +542 têt = -54, +349 +0. et. from - 54 = -(0-3).uz (2-3) 4,-542 = êt 5 +0-3)^2=0, @ 1. Ce 3+ (aicasst +62.5in 5t) - ① x 57 5(0-3) 41 -2542= set 5 -3) +(D-3) = 0 ē 3+ (-a, sin5t.5+ C₂ cosst-5) = ēst (3) D-3 (D-6D+9+25 ) 42 = -5e+ (Cicon5+ + Ca sinist) + Liet -3é3t (c1coss5t +63 sin5+ + 6-6D + 3H) Ug = -5€. Auxiliary equationis m²-6m+34=0. 4 *23*(-54 sin5t +5 c>604.5+ -34 60x5t-36i54 6+ 36-H(34) . -3c, corst - 3G sinot 27 = 625-100 610i, 35iu ein 5+(-56, -362-363) +C0251-(562-34,-34,17 complementary functionia 'u,(C) = (casstt. Ca sin 5t) Particulas Integralies 4(e) = 1 - set. 03-6D+34 40-talebinst (-662-50) +const(5562-6ci1]+7+]

1 4,6)=0 from @ 0- -[0 +(565–66,20] 436)=0.2) 06 4 G © @ wart =0 The le + bg-ogg from 3r@ 2015 *[(-0, sal ooist + coms** - =)] . +20 let Lice) = -* *) sinst - const] tumet. uple) = :05 23sinst the strasst -i et. uzcet) - Le Cost to sinst] et