Problemas de ecuaciones problemario fime
Páginas: 5 (1117 palabras)
Publicado: 3 de febrero de 2012
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]
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[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]
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2) [pic]
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3) [pic]
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[pic][pic]
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4) [pic]
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5) [pic]
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6) [pic] no he termindao
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7) [pic]
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8) [pic]9) [pic]
10) [pic]
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11) Todas las líneas rectas.
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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]
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[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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EJERCICIOS 2.2
Encuentre la solución de las siguientes ecuaciones diferenciales.
1) [pic][pic]
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2) [pic]
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3) [pic]
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[pic][pic]
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4) [pic]
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5) [pic]
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6) [pic]
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7) [pic]
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[pic]...
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]
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[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]
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3) [pic]
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[pic][pic]
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4) [pic]
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5) [pic]
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6) [pic] no he termindao
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7) [pic]
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8) [pic]9) [pic]
10) [pic]
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[pic]
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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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EJERCICIOS 2.2
Encuentre la solución de las siguientes ecuaciones diferenciales.
1) [pic][pic]
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2) [pic]
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3) [pic]
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4) [pic]
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5) [pic]
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6) [pic]
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7) [pic]
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