Answer
( a) It is not linear and first order.
( b) It is linear and first order.
( c) It is not linear and third order.
( d) It is linear and second order.
Work Step by Step
Compare the given equations with the linear equation
$a_{n}(x) y^{(n)}+a_{n-1}(x) y^{(n-1)}+\cdots+a_{1}(x) y^{\prime}+a_{0}(x) y=b(x)$
We see that:
( a) It is not linear and first order. Notice $y^5$ term.
( b) It is linear and first order.
( c) It is not linear and third order. Notice the $\sqrt y$ term.
( d) It is linear and second order.
