EDOS lineares

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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. Resolva as EDOS a seguir:
2. (2x - y) dx - (x + 6y) dy = 0
3. (5x + 4y) dx + (4x - 8y3) dy = 0
4. (y - yx) dx + (cosx+ x cos y − y) dy = 0
5. (2y2x− 3) dx+ (2xy2 + 4) dy = 0
6.
(
2y − 1
x
+ cos 3x
)
dy
dx
+ y
x2 − 4x3 + 3y sin 3x = 0
7. (x+ y)(x− y) dx+ x(x− 2y) dy = 0
8.
(
1 + ln x+ y
x
)
dx = (1− lnx) dy
9. (y3 − y2x− x) dx+ (3xy2 + 2y cosx) dy = 0
10. (x3 + y3) dx+ 3xy2 dy = 0
11. (yln y − e−xy) dx+
(
1
y
+ x ln y
)
dy = 0
12. 2x
y
dx− x2
y2
dy = 0
13. x dy
dx
= 2xex − y + 6x2
14. (3x2y + ey) dx+ (x3 + xey − 2y) dy = 0
15.
(
1− 3
y
+ y
)
dx+
(
1− 3
x
+ x
)
dy = 0
1
16. (ey + 2xy coshx) dx+ xy2x+ y2 coshx = 0
17.
(
x2y3 − 1
1+9x2
)
dx
dy
+ x3y2 = 0
18. (5y - 2x) dy - 2y = 0
19. (x - xy) dx + cosx cos y dy = 0
20. (3xcos 3x+ 3x− 3) dx+ (2y + 5) dy = 0
21. (1 - 2x2 − 2x) dy
dx
= 4x3 + 4xy
22. (2yxcosx− y + 2y2ex) dx = (x−2 x− 4xyex) dy
23. (4x3y − 15x2 − y) dx+ (x4 + 3y2 − x) dy = 0
24.
(
1
x
+ 1
x2 − y
x2+y2
)
dx+
(
yey + x
x2+y2
)
dy = 0
2. Continue
42. y’ = 2y + x(e3x − e2x), y(0) = 2
43. Ldi
dt
+Ri = e, L,R, e ∈ R constantes, i(0) = i0
44. y dx
dy
− x = 2y2, y(1) = 5
45. y’ + (x)y = cos2 x, y(0) = −1
46. dQ
dx
= 5x4Q, Q(0) = −7
47. dT
dt
= k(T − 50), k constante, T (0) = 200
48. x dy + (xy + 2y - 2e−x) dx = 0, y(1) = 0
49. (x+ 1) dy
dx
+ y = lnx, y(1) = 10
50. xy’ + y = e−x, y(1) = 2
51. x(x - 2)y’ + 2y = 0, y(3) = 6
52. x dy
dx
+ (cosx)y = 0, y
(
−π
2
)
= 1
2
53. dy
dx
= y
x−x3 , y(5) = 2
54. cos2 x dy
dx
+ y = 1, y(0) = −3
Resolva as equações de BERNOULLI Nos Problemas 1–6, resolva a equação de
Bernoulli dada.
2. dy
dx
− y = exy2
3. dy
dx
= y(xy3 − 1)
4. x dy
dx
− (1 + x)y = xy2
5. x2 dy
dx
+ y2 = xy
6. 3(1 + x2) dy
dx
= 2xy(y3 − 1)
Nos Problemas 7–10, resolva a equação diferencial dada sujeita à condição
inicial indicada.
8. y1/2 dy
dx
+ y3/2 = 1, y(0) = 4
9. xy(1 + x2) dy
dx
= 1, y(1) = 0
10. 2 dy
dx
= y
x
− x
y2
, y(1) = 1
3