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

Multiple Choice

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

A) $y = - \tan ^ { - 1 } \left( x / c _ { 1 } \right) / c _ { 1 } + c _ { 2 }$
B) $y = c _ { 1 } \int e ^ { x ^ { 2 } } d x + c _ { 2 }$
C) $y = c _ { 1 } e ^ { x } + c _ { 2 }$
D) $y = c _ { 1 } x ^ { 3 } + c _ { 2 }$
E) $y = c _ { 1 } x ^ { 3 } + c _ { 2 } x$