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EDO Lineales de Primer Orden – Reto

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EDO Lineales de Primer Orden – Reto

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Quiz sobre EDOs lineales

Created by

Yeaiza
Yeaiza
Ecuador

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EDO Lineales de Primer Orden – Reto
 

EDO Lineales de Primer Orden – RetoOnline version

Quiz sobre EDOs lineales

by Yeaiza
1

¿Cuál es la forma general de una EDO lineal de primer orden?

2

¿Qué método se usa para resolverla tradicionalmente?

3

¿Qué es μ(x) llamada en este método?

4

¿Cómo se expresa la solución general de la EDO lineal de primer orden?

5

Si p(x)=0, ¿qué tipo de ecuación resulta?

6

Para una condición inicial y(x0)=y0, ¿qué se debe hacer?

7

Propiedad de existencia y unicidad: para p y q continuas en un intervalo, ¿qué sucede?

8

¿Qué representa la constante C en la solución?

9

Si q(x) es constante c, ¿cuál es la solución particular?

10

Sobre el factor integrante, ¿cuál enunciado es correcto?

Explicación

La forma estándar es y' + p(x) y = q(x). La función p(x) acompaña a y.

Se multiplica por μ(x)=exp(∫p dx) para que el lado izquierdo sea derivada.

μ transforma la ecuación en una derivada de μy.

La solución usa el factor integrante μ.

Con p=0 la ecuación se reduce a y' = q(x).

La C se determina a partir de la condición inicial.

Edo lineal de primer orden con coeficientes continuos tiene existencia y unicidad.

C se determina con condiciones iniciales o de frontera.

La solución usa el factor integrante y q constante.

μ convierte la ecuación en una derivada de μy.

 
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