[36] Consider r"(t) = −5x(t)+3y(t), y'(t) = x(t) — 2y(t), x(0) = 2, x'(0) = 7, y(0) = −3. (a) Transform the above initial value problem into algebraic equations for X(s) L{r(t)} and Y(s) = L{y(t)}. (b) Find X (s) and Y(s). = (c) Find the solution of the initial value problem by using r(t) = £¹{X(s)} and y(t) = L ¹{Y(s)}. [36] (a) { $X(5)-25-7-5X(s) + 3Y (s) + 3 - 2Y = = SY (b) X(s) = 222115, Y(s) = 3²5 83 | 282 | 58 (c) r(t) = 1 + e 'cos (2t) + 4e 'sin(2t), y(t) = cos(2t) + 4e 'sin(2t) L
[36] Consider r"(t) = −5x(t)+3y(t), y'(t) = x(t) — 2y(t), x(0) = 2, x'(0) = 7, y(0) = −3. (a) Transform the above initial value problem into algebraic equations for X(s) L{r(t)} and Y(s) = L{y(t)}. (b) Find X (s) and Y(s). = (c) Find the solution of the initial value problem by using r(t) = £¹{X(s)} and y(t) = L ¹{Y(s)}. [36] (a) { $X(5)-25-7-5X(s) + 3Y (s) + 3 - 2Y = = SY (b) X(s) = 222115, Y(s) = 3²5 83 | 282 | 58 (c) r(t) = 1 + e 'cos (2t) + 4e 'sin(2t), y(t) = cos(2t) + 4e 'sin(2t) L
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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Please show work for all parts of this problem, solutions are provided.
![[36] Consider r"(t) = −5x(t)+3y(t), y'(t) = x(t) — 2y(t), x(0) = 2, x'(0) = 7, y(0) = −3.
(a) Transform the above initial value problem into algebraic equations for X(s)
L{r(t)} and Y(s) = L{y(t)}.
(b) Find X (s) and Y(s).
=
(c) Find the solution of the initial value problem by using r(t) = £¹{X(s)} and y(t) =
L ¹{Y(s)}.
[36] (a) { $X(5)-25-7-5X(s) + 3Y (s)
+ 3 - 2Y
=
=
SY
(b) X(s) = 222115, Y(s) = 3²5
83 | 282 | 58
(c) r(t) = 1 + e 'cos (2t) + 4e 'sin(2t), y(t) = cos(2t) + 4e 'sin(2t)
L](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c89c353-252e-4eca-b673-064be33ffdb0%2F960ca777-da7e-42d8-b7d9-4ae49c63cd59%2Fy10easo_processed.png&w=3840&q=75)
Transcribed Image Text:[36] Consider r"(t) = −5x(t)+3y(t), y'(t) = x(t) — 2y(t), x(0) = 2, x'(0) = 7, y(0) = −3.
(a) Transform the above initial value problem into algebraic equations for X(s)
L{r(t)} and Y(s) = L{y(t)}.
(b) Find X (s) and Y(s).
=
(c) Find the solution of the initial value problem by using r(t) = £¹{X(s)} and y(t) =
L ¹{Y(s)}.
[36] (a) { $X(5)-25-7-5X(s) + 3Y (s)
+ 3 - 2Y
=
=
SY
(b) X(s) = 222115, Y(s) = 3²5
83 | 282 | 58
(c) r(t) = 1 + e 'cos (2t) + 4e 'sin(2t), y(t) = cos(2t) + 4e 'sin(2t)
L
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