Linear First Order Differential Equations

Grade 12 Maths Higher — Linear First Order Differential Equations: 25 practice questions with instant scoring and explanations.

1. Standard form of linear first-order DE:
2. The integrating factor for dy/dx + P(x)y = Q(x) is:
3. After multiplying by integrating factor μ(x) = e^(∫P dx), LHS becomes:
4. The solution formula: y = (1/μ(x))∫μ(x)Q(x)dx means:
5. For dy/dx + 2y = e^(-x), the integrating factor is:
6. After multiplying dy/dx + 2y = e^(-x) by μ(x) = e^(2x), we get:
7. Solution of dy/dx + 2y = e^(-x) is:
8. For dy/dx - y = e^x, the integrating factor is:
9. Solution of dy/dx - y = e^x is:
10. For dy/dx + (y/x) = 1, integrating factor is:
11. Solution of dy/dx + (y/x) = 1 is:
12. Newton's Law of Cooling: dT/dt = -k(T - T_m) is:
13. Solution of dT/dt + k·T = k·T_m (k > 0) shows:
14. For dy/dx - (y/x) = x², after solving:
15. Integrating factor method assumes:
16. For dy/dx + P(x)y = Q(x) with initial condition y(a) = b:
17. The solution of dy/dx + y·cot(x) = csc(x) involves:
18. For xy·dy/dx + y² = x², rewritten as dy/dx + (y/x) = (x/y):
19. Variation of parameters for dy/dx + P(x)y = Q(x) applies when:
20. The complementary function for dy/dx + P(x)y = 0 is:
21. For linear DE, superposition principle applies: if y₁, y₂ are solutions:
22. The term 'linear' in linear DE means:
23. For dy/dx + P(x)y = Q(x), the solution y = y_h + y_p where:
24. Review question for Linear First Order Differential Equations
25. Review question for Linear First Order Differential Equations