Linear Methods 3. Find the general solution of the system of differen-tial equationsd12 -4-X =dt8e10t ( cos(2t) – sin(2t)cos(2t)+ 4t³e!0t cos(2t) + sin(2t)sin(2t)-+ 2te'Hint: The characteristic polynomial of the coefficientmatrix is (A – 10)²A + 2².

Given, ddtx=12-428x+2te10tcos2t-sin2tcos2t+4t3e10tcos2t+sin2tsin2t...1 And the given characteristics…

3. Find the general solution of the system of differen- tial equations d 12 -4 X = dt 2 8 + 2te10t cos(2t) – sin(2t) cos(2t) cos(2t) + sin(2t) sin(2t) - + 4t³e!0t Hint: The characteristic polynomial of the coefficient matrix is (A – 10)²A + 2².

3. Find the general solution of the system of differen- tial equations d 12 -4 X = dt 2 8 + 2te10t cos(2t) – sin(2t) cos(2t) cos(2t) + sin(2t) sin(2t) - + 4t³e!0t Hint: The characteristic polynomial of the coefficient matrix is (A – 10)²A + 2².

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

Linear Methods

3. Find the general solution of the system of differen-
tial equations
d
12 -4
-X =
dt
8
e10t ( cos(2t) – sin(2t)
cos(2t)
+ 4t³e!0t cos(2t) + sin(2t)
sin(2t)
-
+ 2te'
Hint: The characteristic polynomial of the coefficient
matrix is (A – 10)²A + 2².

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