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8. Determine order and degree (if defined) of differential equations:
$open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses squared plus cos open parentheses dy over dx close parentheses space equals space 0$

The given differential equation is
$open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses squared plus cos open parentheses dy over dx close parentheses space equals space 0$
The highest order derivative present in the given differential equation is $fraction numerator straight d squared straight y over denominator dx squared end fraction.$ therefore, its order is 2. Since the given differential equation is not a polynomial in $dy over dx.$ therefore, its degree is not defined.