Differential Equations - Solving (variable separable, homogeneous)

Grade 12 Maths — Differential Equations - Solving (variable separable, homogeneous): 25 practice questions with instant scoring and explanations.

1. To solve a separable equation dy/dx = f(x)g(y), we:
2. For dy/dx = 3x²/y, the general solution is:
3. For dy/dx = e^(x+y), the separated form is:
4. For dy/dx = y²/x, the general solution is:
5. For dy/dx = xy with y(0) = 1, the solution is:
6. A homogeneous differential equation has the form:
7. To solve a homogeneous equation, we use the substitution:
8. For the homogeneous equation dy/dx = (x + y)/x, we substitute y = vx to get:
9. For dy/dx = (y/x) + 1 with substitution y = vx, the resulting equation is:
10. The general solution of x(dv/dx) = 1 is:
11. For dy/dx = (x² + y²)/(2xy), this is:
12. For dy/dx = y/x with y(1) = 2, the solution is:
13. The differential equation dy/dx = 1 + y² is:
14. For dy/dx = 1 + y², the separated form is:
15. ∫ dy/(1 + y²) equals:
16. For dy/dx = 1 + y², the general solution is:
17. For dy/dx = (2x + y)/(x − y), substitution v = y/x gives:
18. For the equation dy/dx = y, the general solution is:
19. A differential equation (dy/dx) + 2y/x = 1/x² is:
20. For the linear equation dy/dx + P(x)y = Q(x), the solution is:
21. For dy/dx = sin(x)/y, the general solution is:
22. An exact differential equation M(x,y)dx + N(x,y)dy = 0 satisfies:
23. Question?
24. Question?
25. Question?