Determine order and degree (if defined) of differential equations given in ${{(\frac{{{d}^{2}}y}{d{{x}^{2}}})}^{2}}+\cos (\frac{dy}{dx})=0$
Determine order and degree (if defined) of differential equations given in ${{(\frac{{{d}^{2}}y}{d{{x}^{2}}})}^{2}}+\cos (\frac{dy}{dx})=0$

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

The given differential equation is not a polynomial equation in derivatives as the term  is a T-function of derivative  Therefore the degree is not defined.

Hence, order is 2 and degree is not defined.