Lista E.D.O

Prévia do material em texto

Universidade Federal do Amazonas - UFAM
Lista de exerc´ıcio
E.D.O
1. Formar as equac¸o˜es diferencias das famı´lias de curvas abaixo:
(a) x2 + y2 = C2
(b) y = Cex
(c) x3 = C(x2 − y2)
(d) y = C1 cos(2x) + C2 sin(2x)
(e) y = (C1 + C2x)e
x + C3
(f) y = C1e
2x + C2e
−x
2. Resolva as equac¸o˜es diferencias a varia´veis separa´veis abaixo:
(a) 1x − tan(y) · dydx = 0
(b) 4xy2dx + (x2 + 1)dy = 0
(c) xydx− 3(y − 2)dy = 0
(d) xdx + ye−x
2
dy = 0
(e) (2 + y)dx− (3 − y)dy = 0
(f) xydx− (1 + x2)dy = 0
(g) (1 − x)dy − y2dx = 0
(h) dydx =
e−2y
x2+4
(i) cos2(y) sin(x)dx + sin(y) cos(x)dy = 0
(j) dydx = cos(x + y)