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The non-homogeneous second order differential equation ((2)A ) - y (z) – 4 ( y (z)) + 4 y (z) = 2 e2# sin (z) Y1 (z) = e2# and y2 (z) = e2# z. dz2 has homogeneous fundamental solutions The Wronskian corresponding to these solutions is W(z) = e4z %3D 2(2) f(z) W(z) dz and I2(z) = (2) V1(2) f(x) - W(z) Given the data above, let I (z) where f(z) =2 e2 sin (z). 1) Compute I, (z) and enter your answer in the box below, using Maple syntax (For example, for 3 z2, enter 3*x^2) 1 (2) = 2) Compute I, (z) and enter your answer in the box below, using Maple syntax (For example, for 3 z2, enter 3*x^2) I9 (z) = 3) What does I (z) + I (z) represent? O Another solution to the homogeneous equation associated to the non-homogeneous one The space of all solutions of the non-homogeneous equation O A particular solution of the given non-homogeneous equation

The non-homogeneous second order differential equation ((2)A ) - y (z) – 4 ( y (z)) + 4 y (z) = 2 e2# sin (z) Y1 (z) = e2# and y2 (z) = e2# z. dz2 has homogeneous fundamental solutions The Wronskian corresponding to these solutions is W(z) = e4z %3D 2(2) f(z) W(z) dz and I2(z) = (2) V1(2) f(x) - W(z) Given the data above, let I (z) where f(z) =2 e2 sin (z). 1) Compute I, (z) and enter your answer in the box below, using Maple syntax (For example, for 3 z2, enter 3*x^2) 1 (2) = 2) Compute I, (z) and enter your answer in the box below, using Maple syntax (For example, for 3 z2, enter 3*x^2) I9 (z) = 3) What does I (z) + I (z) represent? O Another solution to the homogeneous equation associated to the non-homogeneous one The space of all solutions of the non-homogeneous equation O A particular solution of the given non-homogeneous equation

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The non-homogeneous second order differential equation y (z) – 4 ( y (z)) + 4 y (z) = 2 e27 sin (z) dz2 has homogeneous fundamental solutions Y1 (z) = e2= and y2 (z) = e2# z. The Wronskian corresponding to these solutions is W(z) = e4z Given the data above, let I, (z) = -V (2) (2) 7(2) W(x) (z) f(=) dz. W(z) dz and 2(1) = V2(x) S = where f(x) =2 e2" sin (z). 1) Compute I, (x) and enter your answer in the box below, using Maple syntax (For example, for 3 z², enter 3*x^2) 1 (z) = 2) Compute I, (z) and enter your answer in the box below, using Maple syntax (For example, for 3 z2, enter 3*x^2) I2 (z) = 3) What does I (z) + I2(z) represent? O Another solution to the homogeneous equation associated to the non-homogeneous one O The space of all solutions of the non-homogeneous equation O A particular solution of the given non-homogeneous equation
Transcribed Image Text:The non-homogeneous second order differential equation y (z) – 4 ( y (z)) + 4 y (z) = 2 e27 sin (z) dz2 has homogeneous fundamental solutions Y1 (z) = e2= and y2 (z) = e2# z. The Wronskian corresponding to these solutions is W(z) = e4z Given the data above, let I, (z) = -V (2) (2) 7(2) W(x) (z) f(=) dz. W(z) dz and 2(1) = V2(x) S = where f(x) =2 e2" sin (z). 1) Compute I, (x) and enter your answer in the box below, using Maple syntax (For example, for 3 z², enter 3*x^2) 1 (z) = 2) Compute I, (z) and enter your answer in the box below, using Maple syntax (For example, for 3 z2, enter 3*x^2) I2 (z) = 3) What does I (z) + I2(z) represent? O Another solution to the homogeneous equation associated to the non-homogeneous one O The space of all solutions of the non-homogeneous equation O A particular solution of the given non-homogeneous equation
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