Answer
( a) It is linear.
( b) It is not linear.
( c) It is not linear.
( d) It is not linear.
( e) It is linear.
( f) It is not linear.
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 linear.
( b) It is not linear. Notice the $y^2$ term.
( c) It is not linear. Notice the $(y')^3$ term.
( d) It is not linear. Notice the $\sin y$ term
( e) It is linear.
( f) It is not linear. Notice the $yy'$ term.
