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rch Rank Page Order 172 5 C (c) u" (t) +8u' (t)+32u(t) = 32 (d) 4u"(t) + 12u' (t) +8u(t) = 8 (e) u' (t) +4u' (t)+3u(t)= 9t (f) u"(t) +4u' (t) +8u(t) = 10 sin(2t) (g) 3u"(t)+15u' (t) + 12u(t) = 10 sin(3t) (h) 3u"(t) + 12u' (t) +39u(t) = 21e-2 cos(4t) (i) 4u"(t) + 12u' (t) +9u(t)=t+t² (j) 3u"(t)+15u' (t) + 12u(t) = 12te-2¹ (k) 4u' (t) +28u' (t) +40u(t) = 16t²e-3t (1) u"(t)+u(t)= t sin(t) (m) u"(t) +2u' (t) +10u(t) = 10e-2t (n) 3u"(t) +6u' (t) +6u(t) = 6e-¹ cos(t) (o) 3u"(t) +12u' (t) +39u(t) = 27te-2t (p) 3u"(t) +24u' (t) +96u(t) = 96 (q) u" (t) +5u' (t) + 4u(t) = 10 sin(2t) (r) 4u"(t) +24u' (t) +20u(t) = 8e-2 (s) u" (t) +7u' (t) + 10u(t) = 15+25t (t) 2u"(t) +4u' (t) + 10u(t) = 6e cos(t) (u) u" (t) +2u' (t) +2u(t) = 25t coś (t) (v) u"(t) +4u' (t) +5u(t) = 40 sin(5t) (w) u"(t)+u(t)=t > 0, Q Q Search Chapter 4. Second-Order Equations

rch Rank Page Order 172 5 C (c) u" (t) +8u' (t)+32u(t) = 32 (d) 4u"(t) + 12u' (t) +8u(t) = 8 (e) u' (t) +4u' (t)+3u(t)= 9t (f) u"(t) +4u' (t) +8u(t) = 10 sin(2t) (g) 3u"(t)+15u' (t) + 12u(t) = 10 sin(3t) (h) 3u"(t) + 12u' (t) +39u(t) = 21e-2 cos(4t) (i) 4u"(t) + 12u' (t) +9u(t)=t+t² (j) 3u"(t)+15u' (t) + 12u(t) = 12te-2¹ (k) 4u' (t) +28u' (t) +40u(t) = 16t²e-3t (1) u"(t)+u(t)= t sin(t) (m) u"(t) +2u' (t) +10u(t) = 10e-2t (n) 3u"(t) +6u' (t) +6u(t) = 6e-¹ cos(t) (o) 3u"(t) +12u' (t) +39u(t) = 27te-2t (p) 3u"(t) +24u' (t) +96u(t) = 96 (q) u" (t) +5u' (t) + 4u(t) = 10 sin(2t) (r) 4u"(t) +24u' (t) +20u(t) = 8e-2 (s) u" (t) +7u' (t) + 10u(t) = 15+25t (t) 2u"(t) +4u' (t) + 10u(t) = 6e cos(t) (u) u" (t) +2u' (t) +2u(t) = 25t coś (t) (v) u"(t) +4u' (t) +5u(t) = 40 sin(5t) (w) u"(t)+u(t)=t > 0, Q Q Search Chapter 4. Second-Order Equations

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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C,r,w do those
Exercise 4.3.1 For each ODE in parts (a)-(w): • Find a general solution un(t) to the homogeneous version of the ODE. • Use the method of undetermined coefficients to find a particular solution up(t) to the nonhomogeneous ODE. This answer is not unique. • Write out a general solution to the nonhomogeneous ODE and use it to obtain initial conditions u(0) = 2 and u' (0) = 3. (a) u" (t) +9u' (t) +20u(t)=2e-3t (b) 4u"(t) + 16u' (t) + 12u(t) = -32e¹ 172 I (c) u" (t) +8u' (t) +32u(t) = 32 tv Chapter 4. Second-Order Equations A B
Transcribed Image Text:Exercise 4.3.1 For each ODE in parts (a)-(w): • Find a general solution un(t) to the homogeneous version of the ODE. • Use the method of undetermined coefficients to find a particular solution up(t) to the nonhomogeneous ODE. This answer is not unique. • Write out a general solution to the nonhomogeneous ODE and use it to obtain initial conditions u(0) = 2 and u' (0) = 3. (a) u" (t) +9u' (t) +20u(t)=2e-3t (b) 4u"(t) + 16u' (t) + 12u(t) = -32e¹ 172 I (c) u" (t) +8u' (t) +32u(t) = 32 tv Chapter 4. Second-Order Equations A B
rch Rank Page Order 172 5 0 (c) u" (t) +8u' (t)+32u(t) = 32 (d) 4u"(t) + 12u' (t) +8u(t) = 8 (e) u' (t) +4u' (t)+3u(t)= 9t (f) u"(t) +4u' (t) +8u(t) = 10 sin(2t) (g) 3u"(t)+15u' (t) + 12u(t) = 10 sin(3t) (h) 3u"(t) + 12u' (t) +39u(t) = 21e-2t cos(4t) (i) 4u"(t) + 12u' (t) +9u(t)=t+t² 20 (j) 3u"(t)+15u' (t) + 12u(t) = 12te-21 (k) 4u' (t) +28u' (t) +40u(t) = 16t²e-3t (1) u"(t)+u(t)= t sin(t) (m) u"(t) +2u' (t) + 10u(t) = 10e-2¹ (n) 3u"(t) +6u' (t) +6u(t) = 6e-¹ cos(t) (o) 3u"(t) +12u' (t) +39u(t) = 27te-2t (p) 3u"(t)+24u' (t) +96u(t) = 96 (q) u" (t) +5u' (t) + 4u(t) = 10 sin(2t) (r) 4u"(t) +24u' (t) +20u(t) = 8e-21 (s) u" (t) +7u' (t) + 10u(t) = 15+25t (t) 2u"(t)+4u' (t) + 10u(t) = 6ecos(t) (u) u" (t) +2u' (t) +2u(t) = 25t coś (t) (v) u'"(t) +4u' (t) +5u(t) = 40 sin(5t) (w) u"(t)+u(t) = t Q Q Search Chapter 4. Second-Order Equations <>
Transcribed Image Text:rch Rank Page Order 172 5 0 (c) u" (t) +8u' (t)+32u(t) = 32 (d) 4u"(t) + 12u' (t) +8u(t) = 8 (e) u' (t) +4u' (t)+3u(t)= 9t (f) u"(t) +4u' (t) +8u(t) = 10 sin(2t) (g) 3u"(t)+15u' (t) + 12u(t) = 10 sin(3t) (h) 3u"(t) + 12u' (t) +39u(t) = 21e-2t cos(4t) (i) 4u"(t) + 12u' (t) +9u(t)=t+t² 20 (j) 3u"(t)+15u' (t) + 12u(t) = 12te-21 (k) 4u' (t) +28u' (t) +40u(t) = 16t²e-3t (1) u"(t)+u(t)= t sin(t) (m) u"(t) +2u' (t) + 10u(t) = 10e-2¹ (n) 3u"(t) +6u' (t) +6u(t) = 6e-¹ cos(t) (o) 3u"(t) +12u' (t) +39u(t) = 27te-2t (p) 3u"(t)+24u' (t) +96u(t) = 96 (q) u" (t) +5u' (t) + 4u(t) = 10 sin(2t) (r) 4u"(t) +24u' (t) +20u(t) = 8e-21 (s) u" (t) +7u' (t) + 10u(t) = 15+25t (t) 2u"(t)+4u' (t) + 10u(t) = 6ecos(t) (u) u" (t) +2u' (t) +2u(t) = 25t coś (t) (v) u'"(t) +4u' (t) +5u(t) = 40 sin(5t) (w) u"(t)+u(t) = t Q Q Search Chapter 4. Second-Order Equations <>
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