Exercise · ZW-SYSTEM-OF-DIFFERENTIAL-EQUATIONS-005 · ★☆☆ Basic
Solve \(x'=2x,\ y'=-3y\) with \(x(0)=1,\ y(0)=2\).
Choose one option.
Show answer
- B. \((e^{2t},\,2e^{-3t})\)
Explanation
The equations are decoupled: \(x=x(0)e^{2t}=e^{2t}\) and \(y=y(0)e^{-3t}=2e^{-3t}\).
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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- ZW-SYSTEM-OF-DIFFERENTIAL-EQUATIONS-009 Which of these systems is decoupled (each equation involves a single unknown)?
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