If y= a cos 2x + b sin 2x , then

Options

A. ` (d^(2)y)/(dx^(2))+y=0`
B. `(d^(2)y)/(dx^(2))+2y =0`
C. `(d^(2)y)/(dx^(2)) -4y =0`
D. ` (d^(2)y)/(dx^(2))+4y =0`

Answer

C

Explanation

The equation of circles touching y -axis at origin is
` (x -alpha)^(2) + ( y -0)^(2) =alpha^(2)`
` Rightarrow x^(2) + alpha^(2) -2alphax + y^(2) = alpha^(2)`
` Rightarrow x^(2)+y^(2) -2alphax =0`
` Rightarrow x + y^(2)/x -2 alphax=0`
Differentiating ` 1+ (x.2y.(dy)/(dx)-y^(2))/x^(2) =0`
` Rightarrow x^(2) +2xy. (dy)/(dx) -y^(2) =0`