CUET Preparation Today
The differential equation of the family of curves $y=asin(bx+c),$ a and c are parameters, is : |
$\frac{d^2y}{dx^2}+b^2y=0 $ $\frac{dy}{dx}+b^2y= 0 $ $\frac{d^2y}{dx^2}-b^2y=0 $ $\frac{d^2y}{dx^2}+y=0 $ |
$\frac{d^2y}{dx^2}+b^2y=0 $ |
The correct answer is option (1) → $\frac{d^2y}{dx^2}+b^2y=0 $ $y=a\sin(bx+c)$ so $\frac{dy}{dx}=ab\cos(bx+c)$ so $\frac{d^2y}{dx^2}=-b^2a\sin(bx+c)=-b^2y$ so $\frac{d^2y}{dx^2}+b^2y=0$ |
