Question

For each of the differential equations given below, indicate its order and degree (if defined).
$open parentheses dy over dx close parentheses cubed minus 4 open parentheses dy over dx close parentheses squared plus 7 straight y equals space sin space straight x$

Solution

The given differential equation is

open parentheses dy over dx close parentheses cubed minus 4 open parentheses dy over dxx close parentheses squared plus 7 straight y space equals space sin space straight x

Since the highest order derivative present in the given differential equation is

dy over dx comma

therefore, order of the equation is 1. Also, index of the highest power of

dy over dx

is 3. So degree is 3.

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