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Question 4. Solve for y(t) given that y" - 16y=32t + 16 subject to y(0) = -6 and y'(0) = 2. (i) write down and solve the associated auxiliary equation (ii) hence determine the natural response function (complementary function). (iii) determine the forced response function (particular integral) (iv) hence find an expression for y(t) which satisfies both the differential equation and the given initial conditions. Note that although the question is in four parts, this is for your guidance only. For this question please just enter your answer for Part (iv), as a function of t in the following box: y(t) = ?

Question 4. Solve for y(t) given that y" - 16y=32t + 16 subject to y(0) = -6 and y'(0) = 2. (i) write down and solve the associated auxiliary equation (ii) hence determine the natural response function (complementary function). (iii) determine the forced response function (particular integral) (iv) hence find an expression for y(t) which satisfies both the differential equation and the given initial conditions. Note that although the question is in four parts, this is for your guidance only. For this question please just enter your answer for Part (iv), as a function of t in the following box: y(t) = ?

Advanced Engineering Mathematics
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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Question 4. Solve for y(t) given that y" - 16y=32t + 16 subject to y(0) = -6 and y'(0) = 2. (i) write down and solve the associated auxiliary equation (ii) hence determine the natural response function (complementary function). (iii) determine the forced response function (particular integral) (iv) hence find an expression for y(t) which satisfies both the differential equation and the given initial conditions. Note that although the question is in four parts, this is for your guidance only. For this question please just enter your answer for Part (iv), as a function of t in the following box: y(t) = /snow FOR E 3 ? Search 5 ||^6 7 8
Transcribed Image Text:Question 4. Solve for y(t) given that y" - 16y=32t + 16 subject to y(0) = -6 and y'(0) = 2. (i) write down and solve the associated auxiliary equation (ii) hence determine the natural response function (complementary function). (iii) determine the forced response function (particular integral) (iv) hence find an expression for y(t) which satisfies both the differential equation and the given initial conditions. Note that although the question is in four parts, this is for your guidance only. For this question please just enter your answer for Part (iv), as a function of t in the following box: y(t) = /snow FOR E 3 ? Search 5 ||^6 7 8
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