Exercise · ZW-SYSTEM-OF-DIFFERENTIAL-EQUATIONS-004 · ★☆☆ Basic
Find the equilibrium point of \(x'=x-y,\ y'=x+y-2\).
Choose one option.
Show answer
- C. \((1,1)\)
Explanation
An equilibrium makes both derivatives vanish: \(x=y\) and \(x+y=2\), so \(x=y=1\).
Review the concept: System of differential equations
A set of \(n\) equations that fix, through a vector function \(\mathbf F\), the derivatives of \(n\) unknown functions \(x_1(t),\dots,x_n(t)\) of a single variable \(t\).
\[\mathbf x'=\mathbf F(t,\mathbf x),\qquad \mathbf x=(x_1,\dots,x_n)\]
More practice problems: system of differential equations
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