Question

The differential equation representing the family of curves $y=A \cos (x+B)$, where $A, B$ are parameters, is

• A. $\frac{ d ^{2} y }{ dx ^{2}}+ y =0$
• B. $\frac{ d ^{2} y }{ dx ^{2}}- y =0$
• C. $\frac{d^{2} y}{d x^{2}}=\frac{d y}{d x}+y$
• D. $\frac{ dy }{ dx }+ y =0$

Answer 1

Answer: (A)

Since $y=A \cos (x+B) $
$\therefore \frac{d y}{d x}=-A \sin (x+B)$
$\Rightarrow \frac{d^{2} y}{d x^{2}}=-A \cos (x+B)=-y$
$ \Rightarrow \frac{d^{2} y}{d x^{2}}+y=0$