The order of the differential equation whose general solution is $y=c_1 \cos 2 x+c_2 \cos ^2 x+c_3 \

Question

The order of the differential equation whose general solution is $y=c_1 \cos 2 x+c_2 \cos ^2 x+c_3 \sin ^2 x+c_4$, is

Professor PC Thomas Classes · Answer

Rewrite using trigonometric identities: $y = c_1\cos 2x + c_2(\frac{1+\cos 2x}{2}) + c_3(\frac{1-\cos 2x}{2}) + c_4 = A\cos 2x + B$. It reduces to 2 independent constants. Thus, order is 2.