Exercise · ZW-SYSTEM-OF-DIFFERENTIAL-EQUATIONS-001 · ★☆☆ Basic

With \(x_1=y\) and \(x_2=y'\), the equation \(y''-3y'+2y=0\) is equivalent to \(\mathbf x'=A\mathbf x\). What is \(A\)?

Choose one option.

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  • B. \(\begin{pmatrix}0&1\\-2&3\end{pmatrix}\)

Explanation

We have \(x_1'=x_2\) and, solving for the top derivative, \(x_2'=y''=-2y+3y'=-2x_1+3x_2\). These rows give \(A=\begin{pmatrix}0&1\\-2&3\end{pmatrix}\).

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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

ZW-SYSTEM-OF-DIFFERENTIAL-EQUATIONS-002 →