यदि ` y = A sin x + B cos x ` तो सिद्ध कीजिए कि ` (d^(2)y)/(dx^(2)) + y = 0 ` है |

Explanation

` :' y = A sin x + B cos x `
` :. (dy)/(dx) = A d/(dx) sin x + B d/dx cos x `
`= A cos x - B sin x `
पुनः अवकलन करने पर ,
` (d^(2)y)/(dx^(2)) = A d/(dx) cos x - B d/dx sin x `
` = -A sin x - B cos x `
` = -(A sin x + B cos x ) `
` = -y`
` (d^(2)y)/(dx^(2)) +y = 0 .`