Question

4. (15 points) Given a system of differential equations \frac{dx}{dt} = (a - 1)x + y \frac{dy}{dt} = -ay Determine conditions on the parameter $a$ such that the origin is a stable node.

          4. (15 points) Given a system of differential equations
\frac{dx}{dt} = (a - 1)x + y
\frac{dy}{dt} = -ay
Determine conditions on the parameter $a$ such that the origin is a stable node.

4. (15 points) Given a system of differential equations
(dx)/(dt) = (a - 1)x + y
(dy)/(dt) = -ay
Determine conditions on the parameter a such that the origin is a stable node.

Added by Jonathan F.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Sri K

12/14/2022

Step 1

Step 1: The system of differential equations can be written in matrix form as: \[ \frac{d}{dt} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} a-1 & 1 \\ 3 & -a \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} \] Show more…

Show all steps

Thanks for your feedback!

4. (15 points) Given a system of differential equations dx =a-1x+y 13 tp - ay Determine conditions on the parameter a such that the origin is a stable node.