A 10 Foot Chain of Weight Density 2 Pounds Per $x ( t )$

A 10 foot chain of weight density 2 pounds per foot is coiled on the ground. One end is pulled upward by a force of 10 pounds. The correct differential equation for the height, $x ( t )$ , of the end of the chain above the ground at time $t$ is

A) $x \frac { d x } { d t } \frac { d ^ { 2 } x } { d t ^ { 2 } } + \frac { d x ^ { 2 } } { d t } + 32 x = 160$
B) $\frac { d x } { d t } \frac { d ^ { 2 } x } { d t ^ { 2 } } + \frac { d x ^ { 2 } } { d t } + 32 x = 160$
C) $x \frac { d ^ { 2 } x } { d t ^ { 2 } } + \frac { d x ^ { 2 } } { d t } + 32 x = 160$
D) $x \frac { d x } { d t } \frac { d ^ { 2 } x } { d t ^ { 2 } } + \frac { d x } { d t } + 32 x = 160$
E) $x \frac { d x } { d t } \frac { d ^ { 2 } x } { d t ^ { 2 } } + \frac { d x ^ { 2 } } { d t } = 160$