यदि ` y=A cos nx + B sin nx,` सिद्ध किजय की
`" "(d^(2)y)/(dx^(2))+n^(2)y=0`

Explanation

यहाँ ` " "y=Acos nx +B sin nx `
`'x'` के सापेक्ष अवकलन करने पर,
`" "(dy)/(dx) =(d)/(dx) (Acos nx)+(d)/(dx) (Bsin nx )`
` " "= Ansin nx +B ncos nx `
` " "= n (B cos nx -Asin nx ) `
पुनः अवकलन करे पर
`" "(d^(2)y)/(dx^(2))=n *(d)/(dx)(Bcos nx -Asin nx )`
` " "= n {B*(d)/(dx) (cos nx )""-A(d)/(dx) (sin nx )}`
` " "= n {-Bnsin nx -An cos nx}`
` " "=- n^(2) {Acos nx + Bsin nx}=-n^(2)y `
` " "d^(2) y//dx^(2) +n^(2) y=0`