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Recall that X = (t)-¹(to)X + $(t) 0-¹(s)F(s) ds solves the initial value problem X' = AX + F(t), X(t) = X₁ whenever (t) is a fundamental matrix of the associated homogeneous system. Use the above to solve the given initial-value problem. * - : -) · ( ) × » - (-:-) , X(1) = -(-₁) X(t) =

Recall that X = (t)-¹(to)X + $(t) 0-¹(s)F(s) ds solves the initial value problem X' = AX + F(t), X(t) = X₁ whenever (t) is a fundamental matrix of the associated homogeneous system. Use the above to solve the given initial-value problem. * - : -) · ( ) × » - (-:-) , X(1) = -(-₁) X(t) =

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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Recall that X = $(t)¶¯¹(to)Xo · + Φ(t) Jto Use the above to solve the given initial-value problem. X(t) = ¹(s)F(s) ds solves the initial value problem X' = AX + F(t), X(t) = X whenever Þ(t) is a fundamental matrix of the associated homogeneous system. t X' = * - (1-1)× - ( 1 ) × » - ( 1) + X(1) = t
Transcribed Image Text:Recall that X = $(t)¶¯¹(to)Xo · + Φ(t) Jto Use the above to solve the given initial-value problem. X(t) = ¹(s)F(s) ds solves the initial value problem X' = AX + F(t), X(t) = X whenever Þ(t) is a fundamental matrix of the associated homogeneous system. t X' = * - (1-1)× - ( 1 ) × » - ( 1) + X(1) = t
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