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-2 -3 Y dY dt 3 -2 (a) Show that the two functions Y1(t) = e=#(cos 3t, sin 3t), Y2(t) = e=#(- sin 3t, cos 3t) are solutions to the differential equation. (b) Solve the initial-value problem -2 -3 Y, dY Y(0) = dt 3 -2 3 ||

-2 -3 Y dY dt 3 -2 (a) Show that the two functions Y1(t) = e=#(cos 3t, sin 3t), Y2(t) = e=#(- sin 3t, cos 3t) are solutions to the differential equation. (b) Solve the initial-value problem -2 -3 Y, dY Y(0) = dt 3 -2 3 ||

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

Consider the linear system.

(a) Show that the two functions Y1(t) =e−2t(cos3t, sin3t), Y2(t) =e−2t(−sin3t, cos3t) are solutions to the differential equation.

(b) Solve the initial-value problem

-2 -3 Y dY dt 3 -2 (a) Show that the two functions Y1(t) = e=#(cos 3t, sin 3t), Y2(t) = e=#(- sin 3t, cos 3t) are solutions to the differential equation. (b) Solve the initial-value problem -2 -3 Y, dY Y(0) = dt 3 -2 3 ||
Transcribed Image Text:-2 -3 Y dY dt 3 -2 (a) Show that the two functions Y1(t) = e=#(cos 3t, sin 3t), Y2(t) = e=#(- sin 3t, cos 3t) are solutions to the differential equation. (b) Solve the initial-value problem -2 -3 Y, dY Y(0) = dt 3 -2 3 ||
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