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Ecuación auxiliar y características

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Ecuación auxiliar y características

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About this activity

Conceptos clave sobre la ecuación auxiliar

Created by

Natasha Cruz Pérez
Natasha Cruz Pérez
Mexico

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Ecuación auxiliar y características
 

Ecuación auxiliar y característicasOnline version

Conceptos clave sobre la ecuación auxiliar

by Natasha Cruz Pérez
1

Si las raíces son complejas r = α ± βi, la solución puede escribirse como e^{α t}(C1 cos(β t) + C2 sin(β t)).

2

Las raíces de la ecuación auxiliar no determinan la forma de la solución.

3

Las raíces repetidas de la ecuación auxiliar introducen términos como t e^{rt} en la solución general.

4

La ecuación auxiliar solo se aplica a ecuaciones de primer orden.

5

Si las raíces son distintas, la solución general es c1 e^{r1 t} + c2 e^{r2 t}.

6

La ecuación auxiliar se obtiene sustituyendo y = sin(rt) en la ecuación diferencial.

7

Si las raíces de la auxiliar son negativas, la solución crece sin límite.

8

La ecuación auxiliar se obtiene sustituyendo y = e^{rt} en la ecuación diferencial con coeficientes constantes.

9

En una EDO lineal con coeficientes constantes, la presencia de raíces repetidas da lugar a términos en t en la solución correspondiente a esa raíz.

10

Si la ecuación auxiliar tiene una raíz real doble r, la solución general es (C1 + C2 t) e^{rt}.

11

Las raíces repetidas solo pueden ocurrir en ecuaciones auxiliares de segundo grado.

12

Al factorizar la ecuación auxiliar, una raíz real doble se representa como (r - r0)^2 como factor.

 
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