Find the Particular Solution of the Differential Equation $4 x y ^ { t } - y = x ^ { 3 } - 2 x \text { that }$

Multiple Choice

Find the particular solution of the differential equation $4 x y ^ { t } - y = x ^ { 3 } - 2 x \text { that }$ satisfies the boundary condition $y \left( \sqrt { \frac { 22 } { 3 } } \right) = 0$ .

A) $y = \frac { x ^ { 3 } } { 3 } - \frac { 2 } { 3 } x$
B) $y = \frac { x ^ { 3 } } { 11 } - \frac { 2 } { 3 } x$
C) $y = \frac { x ^ { 3 } } { 3 } + \frac { 2 } { 11 } x$
D) $y = \frac { x ^ { 3 } } { 3 } - \frac { 2 } { 11 } x$
E) $y = \frac { x ^ { 3 } } { 11 } + \frac { 2 } { 3 } x$