The General Solution of the First-Order Differential Equation $\left( x ^ { 2 } - 1 \right) y ^ { \prime } - x y = x ^ { 3 } - 2 x$

Multiple Choice

The general solution of the first-order differential equation $\left( x ^ { 2 } - 1 \right) y ^ { \prime } - x y = x ^ { 3 } - 2 x$ is

A) $y = x ^ { 2 } + C \sqrt { x ^ { 2 } - 1 }$
B) $y = - x ^ { 2 } + C \sqrt { x ^ { 2 } - 1 }$
C) $y = 2 x ^ { 2 } + C \sqrt { x ^ { 2 } - 1 }$
D) $y = - 2 x ^ { 2 } + C \sqrt { x ^ { 2 } - 1 }$
E) $y = 3 x ^ { 2 } + C \sqrt { x ^ { 2 } - 1 }$