Definition:Linear Second Order Ordinary Differential Equation
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Definition
A linear second order ordinary differential equation is a differential equation which is in (or can be manipulated into) the form:
- $\dfrac {\d^2 y} {\d x^2} + \map P x \dfrac {\d y} {\d x} + \map Q x y = \map R x$
where, as is indicated by the notation, $\map P x$, $\map Q x$ and $\map R x$ are functions of $x$ alone (or constants).
Also presented as
A linear second order ordinary differential equation can also be presented as:
- $\dfrac {\d^2 y} {\d x^2} = \map P x \dfrac {\d y} {\d x} + \map Q x y + \map R x$
Also known as
The order of adjectives can be varied, for example: second order linear ordinary differential equation.
Also see
- Definition:Linear Second Order ODE with Constant Coefficients
- Definition:Homogeneous Linear Second Order ODE
- Results about linear second order ODEs can be found here.
Sources
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 2.10$: Linear Equations
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.14$: Second Order Linear Equations: Introduction