Write out the system of first-order linear differential equations represented by the matrix equation y' = Ay. (Use y_1, y_2, ... for y1, Y2, ... .) 1 0 0 1 - 25 0 Y1 Y2 Уз Does the indicated general solution satisfy the system? Y1 = C1 + Cz cos(5t) + C3 sin(5t) 5C3 cos(5t) – 5C2 sin(5t) -25C2 cos(5t) + 25C3 sin(5t) Y2 = Y3 = Yes O No

Write out the system of first-order linear differential equations represented by the matrix equation y' = Ay. (Use y_1, y_2, ... for y1, Y2, ... .) 1 0 0 1 - 25 0 Y1 Y2 Уз Does the indicated general solution satisfy the system? Y1 = C1 + Cz cos(5t) + C3 sin(5t) 5C3 cos(5t) – 5C2 sin(5t) -25C2 cos(5t) + 25C3 sin(5t) Y2 = Y3 = Yes O No

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Write out the system of first-order linear differential equations represented by the matrix equation y' = Ay. (Use y_1, y_2, ... for y1, Y2, ... .)
1 0
0 1
- 25 0
Y1
Y2
Уз
Does the indicated general solution satisfy the system?
Y1 = C1 +
Cz cos(5t) + C3 sin(5t)
5C3 cos(5t) – 5C2 sin(5t)
-25C2 cos(5t) + 25C3 sin(5t)
Y2 =
Y3 =
Yes
O No

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