1. Consider the system2 -51.-2First verify that5 cos(t)2 cos(t) + sin(t)5 sin(t)72 = 2 sin(t) – cos(t))71)andare solutions of the system. Then(a) show that 7= c,(1) + c27(2) is also a solution of the system for arbitrary c1and c2;%3D(b) show that 1) and (2) form a fundamental set of solutions of the system;(c) find a solution of the system that satisfies the initial condition17(0) = ((d) find W(t) = W[,7](t);(e) show that W = W (t) satisfies the Abel's equation%3DW' = (P1(t) + P22(t))W.|3|

Consider the system 7-()7 2 -5 1 First verify that 5 cos(t) 70 = 2 cos(t) + sin(t) 79 = 5 sin(t) (2sin(t) – cos(t) ) and are solutions of the system. Then (a) show that = c7(1) + c2 T (2) is also a solution of the system for arbitrary c and C2; (b) show that 7(1) and (2) form a fundamental set of solutions of the system; (c) find a solution of the system that satisfies the initial condition 국 (0) = (d) find W(t) = W[70, 7](t); (e) show that W = W(t) satisfies the Abel's equation %3D W' = (P11(t) + P22 (t))W.

Consider the system 7-()7 2 -5 1 First verify that 5 cos(t) 70 = 2 cos(t) + sin(t) 79 = 5 sin(t) (2sin(t) – cos(t) ) and are solutions of the system. Then (a) show that = c7(1) + c2 T (2) is also a solution of the system for arbitrary c and C2; (b) show that 7(1) and (2) form a fundamental set of solutions of the system; (c) find a solution of the system that satisfies the initial condition 국 (0) = (d) find W(t) = W[70, 7](t); (e) show that W = W(t) satisfies the Abel's equation %3D W' = (P11(t) + P22 (t))W.

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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