LISTA_1_-_EDOS separaveis

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INSTITUTO FEDERAL DE EDUCAÇÃO,
CIÊNCIA E TECNOLOGIA DO PIAUÍ - IFPI
CAMPUS Floriano
Engenharia Civil
EDO
Prof. Me. Hilquias Santos
Aluno:
LISTA 1
1.
dy
dx
= sin(5x)
2.
dy
dx
= x+ 13
3. dx+ e3xdy = 0
4. dx− x2dy = 0
5. (x+ 1)
dy
dx
= x+ 6
6.
dy
dx
= 2et
7. xy = 4y
8.
dy
dx
+ 2xy = 0
9.
dy
dx
=
y + 1
x+ 1
10.
dy
dx
=
1 + x
1 + 2y2
11.
dy
dx
= y sinx
12.
dy
dx
= ey(3x+ 2y)
13. (4y + x2y)dy = (2x+ xy2)dx
14. ey = ex + e2−y dy
dx
15. (1 + x2 + y2 + x2y2)dy = y2dx
16. x2y2dy = (y + 1)dx
17. 2y(x+ 1)dy = xdx
1
18.
dy
dx
=
2y + 3
4x+ 5
19. y lnx dy = dx
20.
dS
dt
= kS
21.
dP
dt
= P − P 2
22.
dQ
dt
= k(Q− 70)
23.
dN
dt
+N = Net+2
24. secx dy + csc y dx = 0
25. sin(3x) dx+ 2y cos3(3x) dy = 0
26. e sin(2x) dx+ cosx(e2y − y) dy = 0
27. secx dy = x cot y dx
28. (ex + 1)2eydx+ (ey + 1)exdy = 0
29. y dy = dx
30. (x− 3)dx = (y + 1)3dy
31.
dy
dx
=
12x
y
32.
dy
dx
=
xy + 3x− y − 3
xy − 2x+ 4y − 8
33.
dy
dx
=
xy + 2y − x− 2
xy − 3y + x− 3
34.
dy
dx
= sinx(cos 2y − cos2 y)
35. sec y + sin(x− y) = sin(x+ y)
36. x
√
1− y2 dx = dy
37. (4− 2x3)dy = (4 + x2)dx
38. (x+ 1)dx = (y + 1)dy
2
Problemas 41–48: Resolver com condição inicial
41. (ex + 1) sinx dx = (1 + cosx) dy, y(0) = 0
42. (1 + x)dy + x(1 + 4y2)dx = 0, y(1) = 0
43. y dy = 4x
√
2x+ 1 dx, y(0) = 1
44.
dy
dt
+ y = y, y(1) = 3
45.
dy
dx
= 4(x2 + 1)
46. y(2) = 2
47. x2y′ = y − xy, y(−1) = −1
48. y′ + 2y = 1, y(0) = 0
3