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4. Solve the non-homogeneous systems of ODEs x' = Ax+f(t), with x(a) = xa using the given matrix exponentials. 4 - ( 1 =2), ), f(t) = ( ₁ 5 -2 (a) A = ), x(0) = ( 8 ), e¹² = ½ ( At 18e2t 30e²t -e +5e³t e-t-e³t -5e-t + 5e³t 5e-t-e³t

4. Solve the non-homogeneous systems of ODEs x' = Ax+f(t), with x(a) = xa using the given matrix exponentials. 4 - ( 1 =2), ), f(t) = ( ₁ 5 -2 (a) A = ), x(0) = ( 8 ), e¹² = ½ ( At 18e2t 30e²t -e +5e³t e-t-e³t -5e-t + 5e³t 5e-t-e³t

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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4. Solve the non-homogeneous systems of ODEs x' = Ax+f(t), with x(a) = xa using the given matrix exponentials. 4 -1 - ( 1 = ₂ ), !), f(t) = f(t) = ( 5 -2 (a) A = 18e2t 30e²t ), x(0) = ( 0 ), e4t. At = 1 ( -e-t + 5e³t -5e-t +5e³t e-t-e³t 5e-t e³t
Transcribed Image Text:4. Solve the non-homogeneous systems of ODEs x' = Ax+f(t), with x(a) = xa using the given matrix exponentials. 4 -1 - ( 1 = ₂ ), !), f(t) = f(t) = ( 5 -2 (a) A = 18e2t 30e²t ), x(0) = ( 0 ), e4t. At = 1 ( -e-t + 5e³t -5e-t +5e³t e-t-e³t 5e-t e³t
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