# 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]

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7) [pic]

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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]

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6) [pic]

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8) [pic]

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12) [pic]

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[pic]

EJERCICIOS 2.2

Encuentre la solución de las siguientes ecuaciones diferenciales.

1) [pic][pic]

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2) [pic]

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[pic]

[pic]

[pic]

[pic]

[pic]

3) [pic]

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[pic]

[pic][pic]

[pic]

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[pic]

4) [pic]

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5) [pic]

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[pic]

[pic]

[pic]

[pic][pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

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6) [pic]

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7) [pic]

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