Differential Equations - Variable Separable & Homogeneous

Grade 12 Maths Higher — Differential Equations - Variable Separable & Homogeneous: 25 practice questions with instant scoring and explanations.

1. A variable separable DE has form:
2. For dy/dx = f(x)g(y), we separate as:
3. The solution of dy/dx = e^(x+y) involves:
4. Solving dy/dx = -y/x after separation gives:
5. ∫dy/y = ∫-dx/x gives solution:
6. A homogeneous DE of first order has form:
7. For homogeneous DE, the substitution v = y/x transforms it to:
8. From v = y/x, we have y = vx, so dy/dx =
9. For dy/dx = (y² + x²)/(xy), after substitution v = y/x:
10. The equation dy/dx = (x + y)/(x - y) is:
11. Bernoulli's DE has form:
12. To solve Bernoulli's DE dy/dx + Py = Qy^n (n≠0,1), substitute:
13. The equation dy/dx = (2xy)/(x² - y²) becomes separable after:
14. For dy/dx + y·cot(x) = 2x·csc(x), this is a _____equation:
15. Solution of dy/dx = 1/(x+y) is found by:
16. If dy/dx = f(x+y), substitute v = x + y to get:
17. The solution of xy·dy = (x² + y²)dx becomes variable separable when we use:
18. For xdy - ydx = 0, this is:
19. The solution xdy - ydx = 0 gives:
20. After solving (dy/y) = -(dx/x), we must include:
21. A DE is called exact if:
22. The equation (x² + y)dx + (x + y²)dy = 0 is:
23. For dy/dx + (y/x) = 1/x², the integrating factor is:
24. If integrating factor μ(x) exists and is applied to dy/dx + P(x)y = Q(x):
25. Review question for Differential Equations - Variable Separable & Homogeneous