Answer
The first order differential equations are:
(a) , (c), (d), (f)
Work Step by Step
Since the first order differential equation is the equation that in which the highest derivative is equal to $1$, then
(a) $y'=x^2$ ,
(c ) $\left(y^{\prime}\right)^{3}+y y^{\prime}=\sin x$
(d) $x^{2} y^{\prime}-e^{x} y=\sin y$
(f) $y y^{\prime}+x+y=0$
are first order differential equations.
