Determine order and degree (if defined) of differential equations given in $\frac{{{d}^{2}}y}{d{{x}^{2}}}=\cos 3x+\sin 3x$

The highest order derivative present in the differential equation is  and its order is 2.

The given differential equation is a polynomial equation in derivatives and the highest power raised to highest order  is one, so its degree is 1.

Hence, order is 2 and degree is 1.