Question

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, (??, ?) 24. y'' ? 4y = 0; cosh 2x, sinh 2x, (??, ?) 25. y'' ? 2y' + 5y = 0; ex cos 2x, ex sin 2x, (??, ?) 26. 4y'' ? 4y' + y = 0; ex/2, xex/2, (??, ?) 27. x2y'' ? 6xy' + 12y = 0; x3, x4, (0, ?) 28. x2y'' + xy' + y = 0; cos(ln x), sin(ln x), (0, ?) 29. x3y''' + 6x2y'' + 4xy' ? 4y = 0; x, x?2, x?2 ln x, (0, ?) 30. y(4) + y'' = 0; 1, x, cos x, sin x, (??, ?)

          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, (??, ?)
24. y'' ? 4y = 0; cosh 2x, sinh 2x, (??, ?)
25. y'' ? 2y' + 5y = 0; ex cos 2x, ex sin 2x, (??, ?)
26. 4y'' ? 4y' + y = 0; ex/2, xex/2, (??, ?)
27. x2y'' ? 6xy' + 12y = 0; x3, x4, (0, ?)
28. x2y'' + xy' + y = 0; cos(ln x), sin(ln x), (0, ?)
29. x3y''' + 6x2y'' + 4xy' ? 4y = 0; x, x?2, x?2 ln x, (0, ?)
30. y(4) + y'' = 0; 1, x, cos x, sin x, (??, ?)

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, (??, ?)
24. y” ? 4y = 0; cosh 2x, sinh 2x, (??, ?)
25. y” ? 2y' + 5y = 0; ex cos 2x, ex sin 2x, (??, ?)
26. 4y” ? 4y' + y = 0; ex/2, xex/2, (??, ?)
27. x2y” ? 6xy' + 12y = 0; x3, x4, (0, ?)
28. x2y” + xy' + y = 0; cos(ln x), sin(ln x), (0, ?)
29. x3y”' + 6x2y” + 4xy' ? 4y = 0; x, x?2, x?2 ln x, (0, ?)
30. y(4) + y” = 0; 1, x, cos x, sin x, (??, ?)

Added by Jennifer H.

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