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2. [Medium] (Laplace Transform (System)) Use Laplace transform method to find the PS of $$ \left\{ \begin{array}{l} \begin{bmatrix} x \\ y \end{bmatrix}' = \begin{bmatrix} 3 & -1 \\ 1 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + 25 \begin{bmatrix} \cos t \\ \sin t \end{bmatrix} \\ X(0) = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \end{array} \right. $$

Name: 2 medium laplace transform system use laplace transform method to find the ps of left beginarrayl beginbmatrix x y endbmatrix beginbmatrix 3 1 1 1 endbmatrix beginbmatrix x y endbmatrix 25 b 17796
Uploaded: 2023-12-06T18:59:36-08:00
Duration: 5 min 32 s
Channel: Adi S
Description: 2 medium laplace transform system use laplace transform method to find the ps of left beginarrayl beginbmatrix x y endbmatrix beginbmatrix 3 1 1 1 endbmatrix beginbmatrix x y endbmatrix 25 b 17796

          2. [Medium] (Laplace Transform (System))
Use Laplace transform method to find the PS of
$$ \left\{ \begin{array}{l} \begin{bmatrix} x \\ y \end{bmatrix}' = \begin{bmatrix} 3 & -1 \\ 1 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + 25 \begin{bmatrix} \cos t \\ \sin t \end{bmatrix} \\ X(0) = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \end{array} \right. $$

2 medium laplace transform system use laplace transform method to find the ps of left beginarrayl beginbmatrix x y endbmatrix beginbmatrix 3 1 1 1 endbmatrix beginbmatrix x y endbmatrix 25 b 17796

Added by Melissa S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

12/06/2023

Step 1

The initial condition is $ \mathbf{X}(0) = \begin{bmatrix} 0 \\ 0 \end{bmatrix} $. We will use the Laplace transform method. Let $ \mathcal{L}\{\mathbf{X}(t)\} = \mathbf{X}(s) $. Taking the Laplace transform of both sides of the differential equation: $$ Show more…

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2. [Medium] (Laplace Transform (System)) Use Laplace transform method to find the PS of $$ \left\{ \begin{array}{l} \begin{bmatrix} x \\ y \end{bmatrix}' = \begin{bmatrix} 3 & -1 \\ 1 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + 25 \begin{bmatrix} \cos t \\ \sin t \end{bmatrix} \\ X(0) = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \end{array} \right. $$