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 formwhere each of P, Q, R, G may be any function of the independent variable x (including a constant).
(L23)
Examples of second order ODE's that are not linear, or nonlinear, are
a. b. c. If in some x-interval P(x) is non-zero we can divide equation (L23) by P(x) to obtain
where p = Q/P, etc.
(L24) 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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