1. Given the system-8 -5X'* - ( 3 5 ) *X52(a) Find the general solution.(b) Find the solution that satisfies the initial condition (0) --(3¹). Report your solution as one vector. 2. Given the systemdrI-Ydtdydt171-y(a) Find the general solution.(b) Find the solution that satisfies the initial condition (z(0), y(0)) = (-4,0). Report your solution as one vector.=

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Answered: 1. Given the system -8 -5 X' * - ( 3 5…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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9. ts) Solve the system, and write the solution in vector form. Х1 — х2 + 2хз — Х4 3D 0 + 5x4 X2 = 0
(D^2-(a+b)+ab)y=0,a and b being real and unequal.
Which pair of equations are inverses of each other? A)=Vx-4+ 2. g) = (r-4) 2 B )=v3-x+ 2, gu) = (x – 2 + 3 O) = V1--5, g) = -(« + 5) + 1 D=V-2-1. g(x) =-(x + 1)* + 2
Solve the following system 3 y1 = -yı = -Y1 – 5Y3 233 3/2 1 Y2 +,43 2y3 = (a) yı = cie- + 2c3e2 (b) yı = ce¯* – C3e2 (c) y1 = cie* = cje¯* + 2c3e² (b) y1 = c1e- Y2 = c2e" + cze2* Cze?¤ (c) y1 = c1e¯ 2x Y2 = cze" + c3e2* Cze? C2eª Cze2r 92 = Y3 = 2c3e2 -2x = cje Y3 = 2c3e2" -2x Сзе (е) у1 — Сје Y3 = 2c3e2" (d) ул + 2cze" - -2x Y2 = C2e + C3e“ -2x Y2 = C2e + C3e 2x Y3 2c3e Y3 = 2c3e -2x
3 Find the least squares cubic equation that best fits the points: (-2,-2), (-1, 1), (0, 1), (1, 2), (2, 2).
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Give all solutions of the nonlinear system of equations, including those with nonreal complex components. 71) x2 + y2 = 113 x -y =1 A) {(-8, -7), (-7, -8)} C) {(8,7), (-7,-8)} 71) %3! B) {(8, -7), (7, -8)} D) {(-8,7), (-7,8)}
A parabola y=ax^2 +bx+c passes through the points (1,-1), ( -1, 9 ) and ( 3, 13 ). Determine the values of a, b and c in that equation. Show all your work! Hint! Set up and solve a system of 3 linear equations in 3 unknowns: a, b and c.
2. Solve the linear system algebraically. (2) / 2а — 3b — 5 { b = -1 -x + y= 2 (b) х — Зу 3 1 а — xị + 5x2 = 7 (c) 2.x1 – 7x2 = -3

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1. Given the system -8 -5 X' * - ( 3 5 ) * X 5 2 (a) Find the general solution. (b) Find the solution that satisfies the initial condition (0) - -(3¹). Report your solution as one vector.