Chapter 10.1, Problem 2E

To determine

(a)

Whether the differential equation $y^{\prime }=x^2$ is linear or not.

To determine

(b)

Whether the differential equation $y^{″}=y^2$ linear or not.

To determine

(c)

Whether the differential equation ${(y^{\prime })}^3+y{y}^{\prime }=\sin x$ is linear or not.

To determine

(d)

Whether the differential equation $x^2{y}^{\prime }-e^{x}y=\sin y$ is linear or not.

To determine

(e)

Whether the differential equation $y^{″}+3y^{\prime }=\frac{y}{x}$ islinear or not.

To determine

(f)

Whether the differential equation $y{y}^{\prime }+x+y=0$ is linear or not.