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Given a system of differential equations i) dx dy + dt dt 2 Filho dx dt Show that +x=3√ue™ du which satisfies the initial conditions x(0) = 0 and y(0) = 0 dy dy Ordin(s) ₂2² 281 ~Y=0 LL (s+1)² (s² −2s−1) From (i), determine y(t) by showing that y(t)=2e¹ +te¹ + e -2 cosh √√2t+- « ( -2 3 √2 =sinh V2t JAK

Given a system of differential equations i) dx dy + dt dt 2 Filho dx dt Show that +x=3√ue™ du which satisfies the initial conditions x(0) = 0 and y(0) = 0 dy dy Ordin(s) ₂2² 281 ~Y=0 LL (s+1)² (s² −2s−1) From (i), determine y(t) by showing that y(t)=2e¹ +te¹ + e -2 cosh √√2t+- « ( -2 3 √2 =sinh V2t JAK

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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BUM2 Given a system of differential equations dx dy ·+=+x= dt dt i) dx dy dt x=3√ue™" du which satisfies the initial conditions Fi Show that y=0 28 2 Ordiny(s) = √5 + 1)² (s² -2s-1) x(0) = 0 and y(0) = 0 ne From (i), determine y(t) by showing that 3 y(t) = 2e¹ +te¹ + e' -2 cosh √2t+ =sinh V2t √21) √√2 TIAL
Transcribed Image Text:BUM2 Given a system of differential equations dx dy ·+=+x= dt dt i) dx dy dt x=3√ue™" du which satisfies the initial conditions Fi Show that y=0 28 2 Ordiny(s) = √5 + 1)² (s² -2s-1) x(0) = 0 and y(0) = 0 ne From (i), determine y(t) by showing that 3 y(t) = 2e¹ +te¹ + e' -2 cosh √2t+ =sinh V2t √21) √√2 TIAL
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