Question

Form the differential equation by
eliminating the arbitrary constants if Y
A sinx + B coSX​

Answer 1

Step-by-step explanation:

We have,

$\rm \: y = A \sin(x) + B \cos(x) \: \: ...(i)$

$\implies \rm \: \frac{dy}{dx} = A \cos(x) - B \sin(x) \: \:$

$\implies \rm \: \frac{d^{2} y}{dx^{2} } = - A \sin(x) - B \cos(x) \: \:$

$\implies \rm \: \frac{d^{2} y}{dx^{2} } = - \{A \sin(x) + B \cos(x) \} \: \:$

$\implies \rm \: \frac{d^{2} y}{dx^{2} } = - y \: \: \: [from \: \: (i)]$

$\implies \rm \: \frac{d^{2} y}{dx^{2} } + y = 0 \: \: \:$