Question

The differential equation whose solution is

$y = A \sin x + B \cos x$ is

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

Answer 1

Answer: (A)

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

Answer 2

$y = A \sin x + B \cos x$⇒ $\frac { d y } { d x } = A \cos x - B \sin x$

⇒ $\frac { d ^ { 2 } y } { d x ^ { 2 } } = - A \sin x - B \cos x$ $= - ( A \sin x + B \cos x ) = - y$

⇒ $\frac { d ^ { 2 } y } { d x ^ { 2 } } + y = 0$is the required differential equation.