differential equation

In Problems 23–30 verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the general solution.
23. y” – y’ – 12y = 0; e–3x, e4x, (–8, 8)
24. y” – 4y = 0; cosh 2x, sinh 2x, (–8, 8)
25. y” – 2y’ + 5y = 0; ex cos 2x, ex sin 2x, (–8, 8)
26. 4y” – 4y’ + y = 0; ex/2, xex/2, (–8, 8)
27. x2y” – 6xy’ + 12y = 0; x3, x4, (0, 8)
28. x2y” + xy’ + y = 0; cos(ln x), sin(ln x), (0, 8)
29. x3y'” + 6x2y” + 4xy’ – 4y = 0; x, x–2, x–2 ln x, (0, 8)

30. y(4) + y” = 0; 1, x, cos x, sin x, (–8, 8)