Question

If y = A sin x + B cos X then diffrential equation is given by

Answer 1

Step-by-step explanation:

We have,

$y=A \sin(x) + B \cos(x)\\[tex]</p><p>[tex] \implies \: \frac{dy}{dx} =A \cos(x) - B \sin(x)$

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

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

$\implies \: \frac{d ^{2} y}{d {x}^{2} } = - y$

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