The order of the differential equation whose general solution is `y = c_(1) cos 2x + c_(2) cos^(2) x + c_(3) sin^(2) x + c_(4)` is

Options

A. 2
B. 4
C. 3
D. None of these

Answer

A

Explanation

`y = c_(1) cos 2x + c_(2)cos^(2)x + c_(3) sin^(2) x + c_(4)`
`=c_(1) cos 2x + (c_(2))/(2)(1+cos 2x)+(c_(3))/(2)(1-cos 2x)+c_(4)`
`=((c_(2))/(2)+(c_(3))/(2)+c_(4))+(c_(1)+(c_(2))/(2)-(c_(3))/(2))cos 2x`
`=A + B cos 2x`
That means there are two independent parameter.
Thus, the order of differential equation will be 2.