We have, y=A‌cos‌n‌x+Bsin‌nx On differentiating w.r.t. x, we get y1=−Ansin‌nx+Bn‌cos‌n‌x Again differentiating w.r.t. x, we get ‌y2‌=−An2‌cos‌n‌x−Bn2sin‌nx ⇒‌y2‌=−n2(A‌cos‌n‌x+Bsin‌nx) ⇒‌y2‌=−n2⋅y⇒y2+n2y=0