Problemas de ecuaciones problemario fime

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EJERCICIOS 1.1

Determinar el orden y el grado.

1) [pic] orden 3 y grado 1.



2) [pic] orden 2 y grado 1.



3) [pic] orden 3 y grado 5.



4) [pic]

[pic]

[pic] Orden 3 y grado 1.



5) [pic] orden 2 y grado 1.



6) [pic]

[pic]



[pic]

[pic] Orden 3 y grado 6.



7) [pic]

[pic]

[pic]

[pic]Orden 2 y grado 6.



8) [pic]

[pic]

[pic] Orden 3 y grado 2.



9) [pic]

[pic]

[pic]

[pic] Orden 5 y grado 2.



10) [pic] orden 2 y grado 3.

















EJERCICIOS 1.2

Determinar si la expresión dada es solución o no de la ecuación diferencial dada.

1) [pic] [pic]

[pic] [pic]

[pic]

[pic]No es solución.



2) [pic] [pic]



3) [pic] [pic]

[pic] [pic]

[pic] [pic]

[pic] Si es solución.



4) [pic] [pic]

[pic]

[pic]

[pic]

[pic]

[pic] Si es solución.

5) [pic] [pic]

[pic] [pic]

[pic] Si es solución.



6) [pic] [pic]

[pic] [pic]

[pic]

[pic] Si es solución.7) [pic] [pic]

[pic] [pic]

[pic]

[pic] + [pic]

[pic]

Sustituyendo en la solución.
[pic]








































EJERCICIOS 1.3

Obtenga la ecuación diferencial de las siguientes soluciones generales.

1) [pic]

[pic]



2) [pic]

[pic]

[pic]

[pic]



3) [pic]

[pic]

[pic][pic]

[pic]

[pic]



4) [pic]

[pic]

[pic]

[pic]



5) [pic]

[pic]

[pic]







[pic]

[pic]

[pic]





[pic]

[pic]

[pic]





[pic]

[pic]

[pic]





6) [pic] no he termindao

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]



7) [pic]

[pic]

[pic]

[pic]



8) [pic]9) [pic]



10) [pic]

[pic]

[pic]

[pic]



11) Todas las líneas rectas.

[pic]

[pic]

[pic]



12) Todas las circunferencias de radio=1 y centro en el eje X.





















EJERCICIOS 2.1

Encuentre la solución de las siguientes ecuaciones diferenciales.

1) [pic]

[pic]

[pic]



[pic]



[pic][pic]



5) [pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]



6) [pic]



[pic]



8) [pic]





[pic]







[pic]



[pic]

12) [pic]



[pic]

[pic]















EJERCICIOS 2.2

Encuentre la solución de las siguientes ecuaciones diferenciales.

1) [pic][pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]



2) [pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]





3) [pic]

[pic]

[pic]

[pic]

[pic]

[pic][pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]



4) [pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]



5) [pic]



[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic][pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]



6) [pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]



[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]



7) [pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]...
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