To verify: The equation y ″ + b y ′ + c y = g ( t ) can be written in the factored form ( D − r 1 ) ( D − r 2 ) y = g ( t ) , where r 1 + r 2 = − b and r 1 r 2 = c .

Question

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Answer 1

Question

Chapter 3.5, Problem 35P

(a)

To determine

To verify: The equation y″+by′+cy=g(t) can be written in the factored form (D−r1)(D−r2)y=g(t), where r1+r2=−b and r1r2=c.

(b)

To determine

To show: The solution of equation y″+by′+cy=g(t) can be found by solving following two first order equations (D−r1)u=g(t),(D−r2)y=u(t).

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Page of 2 ZOOM + 1) Answer the following questions by circling TRUE or FALSE (No explanation or work required). i) If A = [1 -2 1] 0 1 6, rank(A) = 3. (TRUE FALSE) LO 0 0] ii) If S = {1,x,x², x³} is a basis for P3, dim(P3) = 4 with the standard operations. (TRUE FALSE) iii) Let u = (1,1) and v = (1,-1) be two vectors in R². They are orthogonal according to the following inner product on R²: (u, v) = U₁V₁ + 2U2V2. ( TRUE FALSE) iv) A set S of vectors in an inner product space V is orthogonal when every pair of vectors in S is orthogonal. (TRUE FALSE) v) Dot product of two perpendicular vectors is zero. (TRUE FALSE) vi) Cross product of two perpendicular vectors is zero. (TRUE FALSE) 2) a) i) Determine which function(s) are solutions of the following linear differential equation. - y (4) — 16y= 0 • 3 cos x • 3 cos 2x -2x • e • 3e2x-4 sin 2x ii) Find the Wronskian for the set of functions that you found from i) as the solution of the differential equation above. iii) What does the result…

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1. Give a subset that satisfies all the following properties simultaneously: Subspace Convex set Affine set Balanced set Symmetric set Hyperspace Hyperplane 2. Give a subset that satisfies some of the conditions mentioned in (1) but not all, with examples. 3. Provide a mathematical example (not just an explanation) of the union of two balanced sets that is not balanced. 4. What is the precise mathematical condition for the union of two hyperspaces to also be a hyperspace? Provide a proof. edited 9:11

Answer 2

Question

Chapter 3.5, Problem 35P

(a)

To determine

To verify: The equation y″+by′+cy=g(t) can be written in the factored form (D−r1)(D−r2)y=g(t), where r1+r2=−b and r1r2=c.

(b)

To determine

To show: The solution of equation y″+by′+cy=g(t) can be found by solving following two first order equations (D−r1)u=g(t),(D−r2)y=u(t).

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Answer 3

Question

Chapter 3.5, Problem 35P

(a)

To determine

To verify: The equation y″+by′+cy=g(t) can be written in the factored form (D−r1)(D−r2)y=g(t), where r1+r2=−b and r1r2=c.

(b)

To determine

To show: The solution of equation y″+by′+cy=g(t) can be found by solving following two first order equations (D−r1)u=g(t),(D−r2)y=u(t).

Expert Solution & Answer

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Answer 4

Question

Chapter 3.5, Problem 35P

(a)

To determine

To verify: The equation y″+by′+cy=g(t) can be written in the factored form (D−r1)(D−r2)y=g(t), where r1+r2=−b and r1r2=c.

(b)

To determine

To show: The solution of equation y″+by′+cy=g(t) can be found by solving following two first order equations (D−r1)u=g(t),(D−r2)y=u(t).

Expert Solution & Answer

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Answer 5

Chapter 3.5, Problem 35P

(a)

To determine

To verify: The equation y″+by′+cy=g(t) can be written in the factored form (D−r1)(D−r2)y=g(t), where r1+r2=−b and r1r2=c.

(b)

To determine

To show: The solution of equation y″+by′+cy=g(t) can be found by solving following two first order equations (D−r1)u=g(t),(D−r2)y=u(t).

Answer 6

Chapter 3.5, Problem 35P

(a)

To determine

To verify: The equation y″+by′+cy=g(t) can be written in the factored form (D−r1)(D−r2)y=g(t), where r1+r2=−b and r1r2=c.

Answer 7

Chapter 3.5, Problem 35P

(a)

To determine

To verify: The equation y″+by′+cy=g(t) can be written in the factored form (D−r1)(D−r2)y=g(t), where r1+r2=−b and r1r2=c.

Answer 8

(b)

To determine

To show: The solution of equation y″+by′+cy=g(t) can be found by solving following two first order equations (D−r1)u=g(t),(D−r2)y=u(t).

Answer 9

(b)

To determine

To show: The solution of equation y″+by′+cy=g(t) can be found by solving following two first order equations (D−r1)u=g(t),(D−r2)y=u(t).

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

To verify: The equation y ″ + b y ′ + c y = g ( t ) can be written in the factored form ( D − r 1 ) ( D − r 2 ) y = g ( t ) , where r 1 + r 2 = − b and r 1 r 2 = c .

To verify: The equation y″+by′+cy=g(t) can be written in the factored form (D−r1)(D−r2)y=g(t), where r1+r2=−b and r1r2=c.

To show: The solution of equation y″+by′+cy=g(t) can be found by solving following two first order equations (D−r1)u=g(t),(D−r2)y=u(t).

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Chapter 3 Solutions