Ecuaciones diferenciales

¡GUÍA DE EJERCICIOS MATEMÁTICA IV Prof. Alain Núñez

TEMA 1: EDO de primer orden

[1] Dado el PVI [pic], [pic].
a) Comprobar que [pic], C constante, es solución de la ecuación diferencial. Clasifíquela y
justifique.
b) Determine dos soluciones del PVI , clasifíquelas y justifique.

[2] Hallar la solucióngeneral.
Variables separables: [pic]
a) [pic] R: [pic]
b) [pic] R: [pic], [pic]
c) [pic] R: [pic]
d) [pic]R: [pic]
e) [pic] R: [pic]
Reducibles a variables separables: [pic]
f) [pic] R: [pic]
g) [pic] R: [pic]
h) [pic]R: [pic]
i) [pic] R: [pic]
j) [pic], y(3) = 2 R: [pic]
k) [pic], y(1) = 2 R: [pic]
l) [pic], y(0)= -1/3 R:[pic]
m) [pic] R: [pic]
n) [pic],
n1) [pic], [pic], [pic]
R:[pic]
n2) Además, [pic] R:[pic]

[3]Determine el grado si son homogéneas.
a) [pic] b) [pic] c) [pic]
d) [pic] e) [pic] f) [pic]
g) [pic] h) [pic] i)[pic] [pic]
j) [pic]

[4] Hallar la solución general.
Homogéneas: [pic]
a) [pic]R: [pic]
b) [pic] R: [pic]
c) [pic] R: [pic]
d) [pic] R: [pic]
Coeficientes lineales
e) [pic]R: [pic]
f) [pic] R: [pic]
g) [pic] R: [pic]
h) [pic] R: [pic]
i) [pic]R: [pic]
j) [pic] R: [pic]
k) [pic] R: [pic]
Exactas

[5] Hallar k tal que las siguientes ecuaciones sean exactas y calcule la solución general.
a) [pic] R: [pic]
b)[pic] R: [pic]
c) [pic] R: [pic]
d) [pic] R: [pic]
e) [pic] R: [pic]
f) [pic] R: [pic]
[6] Hallar la solución...