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If Þ is a normalised fundamental matrix of X = AX at to = 0 and ƒ is continuous in t, then Xp(t) = = [ ²² 0 Þ(t-s)F(s) ds is a particular solution of X = AX+F. Use the above result to find a general solution of 0 2 *- (₁ ) x + (2) X = X (-). -1 3

If Þ is a normalised fundamental matrix of X = AX at to = 0 and ƒ is continuous in t, then Xp(t) = = [ ²² 0 Þ(t-s)F(s) ds is a particular solution of X = AX+F. Use the above result to find a general solution of 0 2 *- (₁ ) x + (2) X = X (-). -1 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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If is a normalised fundamental matrix of X = AX at to = 0 and fis continuous in t, then •t X₂(t) = f ². Þ(t – s)F(s) ds is a particular solution of X = AX+F. Use the above result to find a general solution of X 0 2 = (₁ 3) x + ( ) -1
Transcribed Image Text:If is a normalised fundamental matrix of X = AX at to = 0 and fis continuous in t, then •t X₂(t) = f ². Þ(t – s)F(s) ds is a particular solution of X = AX+F. Use the above result to find a general solution of X 0 2 = (₁ 3) x + ( ) -1
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