Question

The differential equation of the family of curves

$y = a \cos ( x + b )$ is

• A. $\frac { d ^ { 2 } y } { d x ^ { 2 } } - y = 0$
• B. $\frac { d ^ { 2 } y } { d x ^ { 2 } } + y = 0$
• C. $\frac { d ^ { 2 } y } { d x ^ { 2 } } + 2 y = 0$
• D. None of these

Answer 1

Answer: (B)

$\frac { d ^ { 2 } y } { d x ^ { 2 } } + y = 0$

Answer 2

Given equation $y = a \cos ( x + b )$

Differentiate it w.r.t. x we get $\frac { d y } { d x } = - a \sin ( x + b )$

Again $\frac { d ^ { 2 } y } { d x ^ { 2 } } = - a \cos ( x + b ) = - y$ or $\frac { d ^ { 2 } y } { d x ^ { 2 } } + y = 0$ .