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system of first-order equations

Several first-order equations in several unknown functions, coupled together and solved simultaneously.

A system of first-order equations $\mathbf{x}'=A\mathbf{x}$ (the constant-coefficient linear case) collects $n$ unknown functions $x_1(t),\ldots,x_n(t)$ into one vector $\mathbf{x}(t)$ whose derivative is a fixed matrix $A$ times $\mathbf{x}$ itself.

See also

vector-valued solution

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