Find the order and degrees, if defined, of each of the following differential equations:
$straight x space straight y space fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x open parentheses dy over dx close parentheses squared minus straight y dy over dx space equals space 0$

Solution

The given differential equation is

xy fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x open parentheses dy over dx close parentheses squared minus straight y dy over dx equals 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.

So its order is two. It is a polynomial equation in

fraction numerator straight d squared straight y over denominator dx squared end fraction space and space dy over dx

and the highest power raised to

fraction numerator straight d squared straight y over denominator dx squared end fraction

is one, so its degree is one.

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