The General Solution of the First-Order Differential Equation $\left( x ^ { 3 } + x \right) y ^ { \prime } + 4 x ^ { 2 } y = 2$

Multiple Choice

The general solution of the first-order differential equation $\left( x ^ { 3 } + x \right) y ^ { \prime } + 4 x ^ { 2 } y = 2$ is

A) $2 y \left( 1 + x ^ { 2 } \right) ^ { 2 } = x ^ { 2 } + 2 \ln x + C$
B) $x \left( 1 + x ^ { 2 } \right) ^ { 2 } = x ^ { 2 } - 2 \ln x + C$
C) $y \left( 1 + x ^ { 2 } \right) ^ { 2 } = x ^ { 2 } + 2 \ln x + C$
D) $y \left( 1 + x ^ { 2 } \right) ^ { 2 } = x ^ { 2 } - 2 \ln x + C$
E) $x \left( 1 + x ^ { 2 } \right) ^ { 2 } = x ^ { 2 } + 2 \ln x + C$