The initial value problem y ′ ′ + 2 y ′ + 5 y = 10 cos t , y ( 0 ) = 1 , y ′ ( 0 ) = 0 and identify the steady state and transient part of the solution.

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Answer 1

Question

Chapter D2.4, Problem 34E

(a)

To determine

To solve: The initial value problem y′′+2y′+5y=10cost,y(0)=1,y′(0)=0 and identify the steady state and transient part of the solution.

(b)

To determine

To graph: The general solution, steady state solution and transient solution of the differential equation.

(c)

To determine

To state: The time needed to transient time disappear and to confirm that with increasing value of t the solution of the initial value problem approaches the steady state solution.

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Write the given third order linear equation as an equivalent system of first order equations with initial values. Use Y1 = Y, Y2 = y', and y3 = y". - - √ (3t¹ + 3 − t³)y" — y" + (3t² + 3)y' + (3t — 3t¹) y = 1 − 3t² \y(3) = 1, y′(3) = −2, y″(3) = −3 (8) - (888) - with initial values Y = If you don't get this in 3 tries, you can get a hint.

Question 2 1 pts Let A be the value of the triple integral SSS. (x³ y² z) dV where D is the region D bounded by the planes 3z + 5y = 15, 4z — 5y = 20, x = 0, x = 1, and z = 0. Then the value of sin(3A) is -0.003 0.496 -0.408 -0.420 0.384 -0.162 0.367 0.364

Question 1 Let A be the value of the triple integral SSS₂ (x + 22) = 1 pts dV where D is the region in 0, y = 2, y = 2x, z = 0, and the first octant bounded by the planes x z = 1 + 2x + y. Then the value of cos(A/4) is -0.411 0.709 0.067 -0.841 0.578 -0.913 -0.908 -0.120

Answer 2

Question

Chapter D2.4, Problem 34E

(a)

To determine

To solve: The initial value problem y′′+2y′+5y=10cost,y(0)=1,y′(0)=0 and identify the steady state and transient part of the solution.

(b)

To determine

To graph: The general solution, steady state solution and transient solution of the differential equation.

(c)

To determine

To state: The time needed to transient time disappear and to confirm that with increasing value of t the solution of the initial value problem approaches the steady state solution.

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Answer 3

Question

Chapter D2.4, Problem 34E

(a)

To determine

To solve: The initial value problem y′′+2y′+5y=10cost,y(0)=1,y′(0)=0 and identify the steady state and transient part of the solution.

(b)

To determine

To graph: The general solution, steady state solution and transient solution of the differential equation.

(c)

To determine

To state: The time needed to transient time disappear and to confirm that with increasing value of t the solution of the initial value problem approaches the steady state solution.

Expert Solution & Answer

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Answer 4

Question

Chapter D2.4, Problem 34E

(a)

To determine

To solve: The initial value problem y′′+2y′+5y=10cost,y(0)=1,y′(0)=0 and identify the steady state and transient part of the solution.

(b)

To determine

To graph: The general solution, steady state solution and transient solution of the differential equation.

(c)

To determine

To state: The time needed to transient time disappear and to confirm that with increasing value of t the solution of the initial value problem approaches the steady state solution.

Expert Solution & Answer

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Answer 5

Chapter D2.4, Problem 34E

(a)

To determine

To solve: The initial value problem y′′+2y′+5y=10cost,y(0)=1,y′(0)=0 and identify the steady state and transient part of the solution.

(b)

To determine

To graph: The general solution, steady state solution and transient solution of the differential equation.

(c)

To determine

To state: The time needed to transient time disappear and to confirm that with increasing value of t the solution of the initial value problem approaches the steady state solution.

Answer 6

Chapter D2.4, Problem 34E

(a)

To determine

To solve: The initial value problem y′′+2y′+5y=10cost,y(0)=1,y′(0)=0 and identify the steady state and transient part of the solution.

Answer 7

Chapter D2.4, Problem 34E

(a)

To determine

To solve: The initial value problem y′′+2y′+5y=10cost,y(0)=1,y′(0)=0 and identify the steady state and transient part of the solution.

Answer 8

(b)

To determine

To graph: The general solution, steady state solution and transient solution of the differential equation.

Answer 9

(b)

To determine

To graph: The general solution, steady state solution and transient solution of the differential equation.

Answer 10

(c)

To determine

To state: The time needed to transient time disappear and to confirm that with increasing value of t the solution of the initial value problem approaches the steady state solution.

Answer 11

(c)

To determine

To state: The time needed to transient time disappear and to confirm that with increasing value of t the solution of the initial value problem approaches the steady state solution.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. D2.1 - Describe how to find the order of a differential...Ch. D2.1 - Prob. 2E Ch. D2.1 - Prob. 3E Ch. D2.1 - Give a general form of a second-order linear...Ch. D2.1 - Prob. 5E Ch. D2.1 - Prob. 6E Ch. D2.1 - Prob. 7E Ch. D2.1 - Prob. 8E Ch. D2.1 - Prob. 9E Ch. D2.1 - Prob. 10E

The initial value problem y ′ ′ + 2 y ′ + 5 y = 10 cos t , y ( 0 ) = 1 , y ′ ( 0 ) = 0 and identify the steady state and transient part of the solution.

Solution Summary: The author explains how to solve the initial value problem and identify the steady state and transient part of the solution.

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To solve: The initial value problem y′′+2y′+5y=10cost,y(0)=1,y′(0)=0 and identify the steady state and transient part of the solution.

To graph: The general solution, steady state solution and transient solution of the differential equation.

To state: The time needed to transient time disappear and to confirm that with increasing value of t the solution of the initial value problem approaches the steady state solution.

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Chapter D2 Solutions