Ordinary differential equations order and degree - Question Bank

1. What is the degree of the differential equation (d^2y/dx^2)^2 + (dy/dx)^2 = x?
A) 1
B) 2
C) 3
D) 4
2. The order of the differential equation d^3y/dx^3 + (dy/dx) + y = 0 is:
A) 1
B) 2
C) 3
D) 0
3. Determine the degree of the differential equation dy/dx = y.
A) 0
B) 1
C) 2
D) 3
4. What is the order of the differential equation d^2y/dx^2 + x^2y = 0?
A) 1
B) 2
C) 3
D) 0
5. The degree of the differential equation (d^3y/dx^3) + 2(d^2y/dx^2) + dy/dx = 0 is:
A) 1
B) 2
C) 3
D) 6
6. Find the order of the differential equation d^4y/dx^4 + dy/dx = sin(x).
A) 1
B) 2
C) 3
D) 4
7. What is the degree of the differential equation x(dy/dx) + y = x?
A) 0
B) 1
C) 2
D) 3
8. The order of the differential equation d^2y/dx^2 + y = 0 is:
A) 1
B) 2
C) 3
D) 0
9. Determine the degree of the differential equation (dy/dx)^2 + x(dy/dx) + y = 0.
A) 0
B) 1
C) 2
D) 3
10. What is the order of the differential equation dy/dx = cos(x)?
A) 0
B) 1
C) 2
D) 3
11. The degree of the differential equation (d^2y/dx^2)^3 + (dy/dx)^2 = 0 is:
A) 1
B) 2
C) 3
D) 6
12. Find the order of the differential equation d^3y/dx^3 = x + dy/dx.
A) 1
B) 2
C) 3
D) 0
13. What is the degree of the differential equation dy/dx + y^2 = x?
A) 0
B) 1
C) 2
D) 3
14. The order of the differential equation d^2y/dx^2 + 5(dy/dx) = 0 is:
A) 1
B) 2
C) 3
D) 0
15. Determine the degree of the differential equation x(dy/dx) + y = x^2.
A) 0
B) 1
C) 2
D) 3
16. What is the order of the differential equation dy/dx = y/x?
A) 0
B) 1
C) 2
D) 3
17. The degree of the differential equation (d^2y/dx^2)^1/2 = dy/dx is:
A) 1
B) 2
C) 3
D) 4
18. Find the order of the differential equation y''' + y'' + y' + y = 0.
A) 1
B) 2
C) 3
D) 4
19. What is the degree of the differential equation d^3y/dx^3 = (dy/dx)^2?
A) 1
B) 2
C) 3
D) 6
20. The order of the differential equation d^4y/dx^4 + y = 0 is:
A) 1
B) 2
C) 3
D) 4
21. Determine the degree of the differential equation d^2y/dx^2 + (dy/dx)^3 = x.
A) 1
B) 2
C) 3
D) 4
22. What is the order of the differential equation dy/dx = sqrt(y)?
A) 0
B) 1
C) 2
D) 3
23. The degree of the differential equation (dy/dx) + y = x is:
A) 0
B) 1
C) 2
D) 3
24. Find the order of the differential equation y'' + y' = x.
A) 1
B) 2
C) 3
D) 0
25. What is the degree of the differential equation (d^3y/dx^3)^2 + (d^2y/dx^2) + dy/dx = 0?
A) 1
B) 2
C) 3
D) 6
26. The order of the differential equation d^2y/dx^2 + 2(dy/dx)^2 + y = 0 is:
A) 1
B) 2
C) 3
D) 4
27. Determine the degree of the differential equation dy/dx = x.
A) 0
B) 1
C) 2
D) 3
28. What is the order of the differential equation (dy/dx)^3 = x^2 + y?
A) 1
B) 2
C) 3
D) 0
29. The degree of the differential equation (d^3y/dx^3) + (dy/dx)^2 = 0 is:
A) 1
B) 2
C) 3
D) 6
30. Find the order of the differential equation d^2y/dx^2 + x(dy/dx) + y = sin(x).
A) 1
B) 2
C) 3
D) 0
31. What is the degree of the differential equation y = x(dy/dx) + (dy/dx)^2?
A) 0
B) 1
C) 2
D) 3
32. The order of the differential equation sin(x) dx + cos(y) dy = 0 is:
A) 0
B) 1
C) 2
D) 3
33. Determine the degree of the differential equation (d^2y/dx^2)^2 = dy/dx - 1.
A) 1
B) 2
C) 3
D) 4
34. What is the order of the differential equation d^5y/dx^5 + y = 0?
A) 1
B) 3
C) 5
D) 0
35. The degree of the differential equation dy/dx = y is:
A) 0
B) 1
C) 2
D) 3
36. Find the order of the differential equation y'' = (1 + (y')^2)^(3/2).
A) 1
B) 2
C) 3
D) 4
37. What is the degree of the differential equation d^2y/dx^2 = y + (dy/dx)^2?
A) 1
B) 2
C) 3
D) 4
38. The order of the differential equation (dy/dx)^2 + y = x is:
A) 0
B) 1
C) 2
D) 3
39. Determine the degree of the differential equation d^2y/dx^2 + dy/dx + sin(y) = 0.
A) 1
B) 2
C) 3
D) Undefined
40. What is the order of the differential equation d^3y/dx^3 + 2(d^2y/dx^2) + dy/dx = e^x?
A) 1
B) 2
C) 3
D) 0
41. The degree of the differential equation dy/dx + y = x dy/dx is:
A) 0
B) 1
C) 2
D) 3
42. Find the order of the differential equation x(d^2y/dx^2) + x^2(dy/dx) + y = 0.
A) 1
B) 2
C) 3
D) 4
43. What is the degree of the differential equation (d^2y/dx^2)^1/2 + dy/dx = 0?
A) 1
B) 2
C) 3
D) 4
44. The differential equation xy'' + y' + y = x^2 has an order of:
A) 1
B) 2
C) 3
D) 0
45. Determine the degree of the differential equation sqrt(1 + (dy/dx)^2) = a(d^2y/dx^2).
A) 1
B) 2
C) 3
D) 4
46. What is the order of the differential equation d^4y/dx^4 = cos(x)?
A) 1
B) 2
C) 3
D) 4
47. The degree of the differential equation (dy/dx)^3 + dy/dx - x = 0 is:
A) 1
B) 2
C) 3
D) 4
48. Find the order of the differential equation y'' + 5y' - 6y = 0.
A) 1
B) 2
C) 3
D) 0
49. What is the degree of the differential equation dy/dx = sin(x)?
A) 0
B) 1
C) 2
D) Undefined
50. The order of the differential equation (d^3y/dx^3)^2 + (d^2y/dx^2)^3 + dy/dx + y = 0 is:
A) 1
B) 2
C) 3
D) 6
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