Differential Equations - Order, Degree, Formation

Grade 12 Maths Higher — Differential Equations - Order, Degree, Formation: 25 practice questions with instant scoring and explanations.

1. A differential equation is an equation involving:
2. The order of a differential equation is the:
3. The degree of a differential equation is the:
4. The equation d²y/dx² + 3(dy/dx)² = x has order and degree:
5. (d³y/dx³)² + 3dy/dx = x has order and degree:
6. A general solution of n-th order DE contains:
7. A particular solution is obtained from general solution by:
8. Forming DE from y = Ae^(2x) + Be^(-2x) eliminates:
9. To eliminate arbitrary constants from y = Cx + C², we:
10. If y = ax + b, eliminating a and b requires:
11. The DE formed from y = A cos(x) + B sin(x) is:
12. The solution of dy/dx = k (constant) is:
13. A linear differential equation of first order has form:
14. The equation (d²y/dx²)² = (dy/dx)³ is of order and degree:
15. A singular solution is one that:
16. The general solution y = Ax + B of DE y = x(dy/dx) + (dy/dx)² is:
17. Degree is not defined when the DE:
18. The DE (dy/dx)^(1/2) + y = 0 has order and degree:
19. To form DE from y = e^(ax), we apply:
20. The family of curves x² + y² = a² represents:
21. Total differential df = (∂f/∂x)dx + (∂f/∂y)dy when applied to y = ax gives:
22. A non-linear DE example is:
23. The DE from y = c₁e^(2x) + c₂e^(-2x) is:
24. Standard form of 2nd order linear DE is:
25. Review question for Differential Equations - Order, Degree, Formation