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Vector Differential Equation

A vector differential equation is a differential equation whose unknown is a vector-valued function. A first-order system can be written

x^'(t)=f(t,x(t)).

A collection of scalar ordinary differential equations can therefore be regarded as one vector differential equation. When the right-hand side is linear, the equation has the form

x^'(t)=A(t)x(t)+b(t),

which is the vector form associated with a matrix differential equation.

See also

Matrix Differential Equation, Ordinary Differential Equation

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References

Boyce, W. E. and DiPrima, R. C. Elementary Differential Equations and Boundary Value Problems, 9th ed. Hoboken, NJ: Wiley, 2009.

Cite this as:

Weisstein, Eric W. "Vector Differential Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/VectorDifferentialEquation.html

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