Show-that-for-any-arbitary-constants-A-and-B-y-A-sinx-1-x-cosx-B-cosx-1-x-sinx-satisfy-the-differential-equation-d-2-y-dx-2-1-2-x-2-y-0-

Question Number 9011 by tawakalitu last updated on 13/Nov/16

Show that for any arbitary constants A and B

y = A (sinx + \frac{1}{x} cosx) + B (cosx - \frac{1}{x} sinx) satisfy

the differential equation \frac{d^{2} y}{{dx}^{2}} + (1 - \frac{2}{x^{2}}) y = 0