What is the order of the differential equation whose general solution is `y=c_(1)cos2x+c_(2)sin^(2)x+c_(3)cos^(2)x+c_(4)e^(2x)+c_(5)e^(2x+c6)`?

Explanation

`y=c_(1)cos2x+c_(2)2sin^(2)x+c_(3)cos^(2)x+c_(4)e^(2x)+c_(5)e^(2x+c6)`
`c_(1)cos2x+c_(2)(1-cos2x)/(2)+c_(3)(cos2x+1)/(2) + c_(4)e^(2x)+c_(5)e^(c6)e^(2x)`
`=(c_(1)-c_(2)/2+c_(3)/2)cos2x+(c_(2)/2+c_(3)2)+(c_(4)+c_(5)e^(c6))e^(2x)`
`=lambda_(1)cos2x+lambda_(2)e^(2x)+lambda_(3)`
So, number of artibatry constants in the equation is 3.
Therefore, order of the differential equation will be 3.