University:
Georgia Southern University
Course:
MATH 3230 | Ordinary Differential Equations
Academic year:

2024
Views:

368

Pages:

4
Author:

Jalen W.

Definition Suppose we have the linear system, ( x 0 (t) = a1 x(t) + b1 y (t) + f (t) , y 0 (t) = a2 x(t) + b2 y (t) + g (t) with initial values x(0) = x0 and y (0) = y0 . The Laplace Transform of the system becomes, ( sX (s) − x(0) = a1 X (s) + b1 Y (s) + F (s) , sY (s) − y (0) = a2 X (s) + b2 Y (s) + G (s) which can be solved to get ( b1 Y (s) + X (s) = s−a 1 a2 Y (s) = s−b2 X (s) + x(0) 1 s−a1 F (s) + s−a1 y (0) 1 s−b2 G (s) + s−b2 . Example Solve the linear system. Suppose x(0) = 3 and y (0) = 2. ( x 0 (t) = 2x(t) + 0y (t) + e t y 0 (t) = 0(t) + 3y (t) − e t Example Solve the linear system. Suppose x(0) = 1 and y (0) = 2. ( x 0 (t) = x(t) + y (t) y 0 (t) = −2x(t) + 4y (t) Example Solve the linear system. Suppose x(0) = 1 and y (0) = 2. ( x 0 (t) = 0x(t) + 2y (t) + e t y 0 (t) = −x(t) + 3y (t) − e t

Section 9.2: Solving Linear Systems.pdf

Section 9.2: Solving Linear Systems.pdf - Page 3

Section 9.2: Solving Linear Systems.pdf - Page 4

of 4

Details

Description

Struggling with your assignment and deadlines?

Free up your schedule!

Take 5 seconds to unlock