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# The differential equation for y = A cos αx + B sin αx,

Question:

The differential equation for = A cos α+ B sin αx, where A and B are arbitrary constants is

(A) $\frac{d^{2} y}{d x^{2}}-\alpha^{2} y=0$

(B) $\frac{d^{2} y}{d x^{2}}+\alpha^{2} y=0$

(C) $\frac{d^{2} y}{d x^{2}}+\alpha y=0$

(D) $\frac{d^{2} y}{d x^{2}}-\alpha y=0$

Solution:

Correct option is (B).

Given equation is = A cos a+ B sin ax

Differentiating both sides w.r.t. x, we have