CUET Preparation Today
The differential equation for which $y=a\, cos \, x + b \, sin \, x $ is a solution, is |
$\frac{d^2y}{dx^2}+y = 0 $ $\frac{d^y}{dx^2}-y = 0 $ $\frac{d^y}{dx^2}+ (a + b ) y = 0 $ $\frac{d^y }{dx^2}+ (a-b) y = 0 $ |
$\frac{d^2y}{dx^2}+y = 0 $ |
The correct answer is option (1) : $\frac{d^y}{dx^2}+y = 0 $ We have, $y=acosx + b sin x$ $⇒\frac{dy}{dx}= - a sin x + b \, cos x$ $⇒\frac{d^2y}{dx^2}=-acos x - b sin x $ $⇒\frac{d^2y }{dx^2}=-y $ |
