Definition:Reduced Equation of Linear ODE with Constant Coefficients/Second Order
< Definition:Reduced Equation of Linear ODE with Constant Coefficients(Redirected from Definition:Reduced Equation of Linear Second Order ODE With Constant Coefficients)
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Definition
Consider the linear second order ODE with constant coefficients:
- $(1): \quad \dfrac {\d^2 y} {\d x^2} + p \dfrac {\d y} {\d x} + q y = \map R x$
The equation:
- $\dfrac {\d^2 y} {\d x^2} + p \dfrac {\d y} {\d x} + q y = 0$
is the reduced equation of $(1)$.
Sources
- 1958: G.E.H. Reuter: Elementary Differential Equations & Operators ... (previous) ... (next): Chapter $1$: Linear Differential Equations with Constant Coefficients: $\S 2$. The second order equation: $\S 2.1$ The reduced equation