Question

Problem 3. (1 point) Find y as a function of tif y" + 5y - 14y = 0, y(0) = 5, y(1) = 6, y) = Remark: The initial conditions involve values at two points. Problem 4. (1 point) Find the solution to the linear system of differential equations 8x - 15y 6x-lly satisfying the initial conditions x(0) = -16 and yo) = -10 x(t) = Note: You can earn partial credit on this problem

Answer 1

S. 0 Giren ytsyl- 14y=0, y co)=5, y ci)=6 mitsm14=0 is an Auxillary equation mtim-2m-1450 mim+7)-2 (m+1)=0 m=2"] 2 r g(x)= qonut ca era y'(x) = 298 267 xe kaitse'st chti2= 5 Xe 70-5 4 (1) = 6 Glee). 51-6 (2= БеY 6 2 -1 e-e and G = 5-12 ber (527-82 +6 2 5 (seho -7 be-5e er e er 6-577 G = e e e .e -72 2x (sero) Gal 1 ... y(x) = [(6-57):24 7 30 CS Scanned with CamScanner

2 2 = 84-15y of 4-8x+15420 (08)*+159 = } y'a Gailly (D+1) y -62 zo- x 6 15y =0 from ① 89 (0-8)4+ -0 X(0-8) -G5 +(D+1124 (90+ 0-8D+110-88) 9 = 0 (o'+3D+2)y = 0 Auxillary cauation mit 3m +2=0 mtzm+m+220 mim+2)+1(m+2)=0 - m=-1, 2 -2+ g(x) = cette from Ola (0-8)* + 15y = (D-3)* +15=0 X(0+1) Ĉ O x 15 ont + lotny 220 (54110 – 80 -88 +90) a (0'+30+2)9 20 ecuation m +3m +2=0 Marl, -2 2. alt)= a et ta ezt Aurillary equation CS Scanned with CamScanner