Math Link 2: Linear and non - linear second order ordinary differential equations.

Let x, y be real variables.

A second order ordinary differential equation (ODE) is said to be linear if it is of the form
(L23)
where each of P, Q, R, G may be any function of the independent variable x (including a constant).

Examples of second order ODE's that are not linear, or nonlinear, are
a.
b.
c.

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If in some x-interval P(x) is non-zero we can divide equation (L23) by P(x) to obtain

(L24)
where p = Q/P, etc.

Equation (L24) is often called the standard form of the second order linear ordinary ODE.

Equation (L24) is said to homogeneous if g(x) = 0; if not, it is said to be non-homogeneous.


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