Differential Equations

Maths, HSSC-KPK Second Year. This chapter is split into 30 topics and has 685 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Order of a differential equation 26 questions
2. Separable equations: initial value problems 24 questions
3. Degree of a differential equation 25 questions
4. Is a first order equation homogeneous? 22 questions
5. Limited growth: time to reach a given level 21 questions
6. Limited growth: dy/dt = k(N - y) 22 questions
7. Finding the particular solution from a family of curves 24 questions
8. Verifying that a function is a solution 21 questions
9. Reducing to homogeneous form and homogeneous IVPs 20 questions
10. Differential equation: definition and ODE versus PDE 24 questions
11. Exponential decay, half-life and continuous growth 23 questions
12. Exercise 9.2: rate and application problems 23 questions
13. The substitution y = ux for homogeneous equations 23 questions
14. Formation of a differential equation from a rate problem 21 questions
15. Homogeneous functions and their degree 29 questions
16. Reducing a differential equation to linear form 20 questions
17. Equations reducible to separable form: the substitution 24 questions
18. Exercise 9.2: separable equations (Question 1 type) 20 questions
19. Orthogonal trajectories: finding the second family 21 questions
20. Initial value problems solved by direct integration 23 questions
21. Orthogonal trajectories: definition and slope condition 21 questions
22. Solving homogeneous differential equations 20 questions
23. Equations reducible to separable form: solutions 20 questions
24. Separation of variables: concept 20 questions
25. Bacterial growth: finding k and the time for a multiple 23 questions
26. Separable equations: general solutions 30 questions
27. Natural growth and decay: the model dy/dt = ky 21 questions
28. Order and degree together 25 questions
29. Linear and non-linear differential equations 24 questions
30. General solution, particular solution and initial value problem 25 questions