Question

01: Solve the following D.Es: 1) dy dx e3x+y 2) y(6) + 12y(4) + 48y(2) + 64y = 0)

Answer 1

QI, ile dų da 3x+4 = e dy 336+4 ге da Divide both sides by y 3x éy dy- é Integrate both sides with respect to o. Seu dy dal - Sest de da 32 -Y -e e 3 tci 321 e 3 C 3x e-9 y = -log[*-ci] -log [ er te 32 y(«) CS Scanned with CamScanner

2, y(b?+12ycu? (2) + usy +644 =0. It is higher order homogenous differential equations. (0+ 0 12D 0 120+ 48 D D²+64)y=0. Dy=-E-5-21 D57E-5 +2i D = 21 D2 = -21 - D3 = - E-5+2i Do=E-5-21 -E-5 -E-5 sin(at) +Cze é cedo cos(26) + Cue y = C, COS (26) + casin (21) + E-5 sin (26) +(50 e E-SCOS(26) + CS Scanned with CamScanner
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