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Differential Equations2D

Systems of Differential Equations - Theory & Concepts - Systems Of Des

Solving systems of linear differential equations using elimination, matrix methods (eigenvalues), and phase portrait analysis.

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Phase Portrait

(x′y′)=(−1.0−1.01.0−1.0)(xy)\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} -1.0 & -1.0 \\ 1.0 & -1.0 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}
Critical Point (0,0): Stable Spiral
-1.0
-1.0
1.0
-1.0
Tr(A)=−2.00\text{Tr}(A) = -2.00
det⁡(A)=2.00\det(A) = 2.00
Δ=Tr2−4det⁡=−4.00\Delta = \text{Tr}^2 - 4\det = -4.00
x range: [-5, 5]

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