A Solution of the Equation for the Differential Equation $y ^ { \prime \prime } = 2 x \left( y ^ { \prime } \right) ^ { 2 }$

Multiple Choice

A solution of the equation for the differential equation $y ^ { \prime \prime } = 2 x \left( y ^ { \prime } \right) ^ { 2 }$ is

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