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In Exercises 5-8, the linear systems are the same as those in Exercises 1-4. For each system, (a) find the general solution: (b) find the particular solution for the initial condition Y₁ = (1, 0); and (e) sketch the x(t)- and y(t)-graphs of the solution. (Compare these sketches with the sketches you obtained in the corresponding problem from Exercises 1-4.) ¥-(-31)x - (-_-_-_¹ ) x dY 5. $ 4-(1-9) -3 7. 2-(22) x Y dY dY dt dY dt

In Exercises 5-8, the linear systems are the same as those in Exercises 1-4. For each system, (a) find the general solution: (b) find the particular solution for the initial condition Y₁ = (1, 0); and (e) sketch the x(t)- and y(t)-graphs of the solution. (Compare these sketches with the sketches you obtained in the corresponding problem from Exercises 1-4.) ¥-(-31)x - (-_-_-_¹ ) x dY 5. $ 4-(1-9) -3 7. 2-(22) x Y dY dY dt dY dt

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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HELP !! 7 & 9 please !

In Exercises 5-8, the linear systems are the same as those in Exercises 1-4. For each system, (a) find the general solution; (b) find the particular solution for the initial condition Y₁ = (1, 0); and (c) sketch the x (t)- and y(t)-graphs of the solution. (Compare these sketches with the sketches you obtained in the corresponding problem from Exercises 1-4.) dY -3 0 $ 27-(-; -;) x 5. Y dt 1 -3 7. dY dt = -2 (71)x 1-4 dY 2 1 **-(-3) v Y dt -1 4 6. 8. dY dt 0 1 - ( _-; _¹' ) x Y -1 -2 9. Given a quadratic λ² + aλ + ß, what condition on a and ß guarantees (a) that the quadratic has a double root? (b) that the quadratic has zero as a root?
Transcribed Image Text:In Exercises 5-8, the linear systems are the same as those in Exercises 1-4. For each system, (a) find the general solution; (b) find the particular solution for the initial condition Y₁ = (1, 0); and (c) sketch the x (t)- and y(t)-graphs of the solution. (Compare these sketches with the sketches you obtained in the corresponding problem from Exercises 1-4.) dY -3 0 $ 27-(-; -;) x 5. Y dt 1 -3 7. dY dt = -2 (71)x 1-4 dY 2 1 **-(-3) v Y dt -1 4 6. 8. dY dt 0 1 - ( _-; _¹' ) x Y -1 -2 9. Given a quadratic λ² + aλ + ß, what condition on a and ß guarantees (a) that the quadratic has a double root? (b) that the quadratic has zero as a root?
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