The Particular Solution of the Differential Equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } = 12 x ^ { 2 }$

Multiple Choice

The particular solution of the differential equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } = 12 x ^ { 2 }$ satisfying the boundary conditions when x = 0, y = 1 and x = 3, y' = 8 is

A) $y = x ^ { 4 } - \frac { 8 } { 3 } x + 1$
B) $y = x ^ { 4 } - \frac { 1 } { 3 } x + 1$
C) $y = x ^ { 4 } - \frac { 74 } { 3 } x + 1$
D) $y = x ^ { 4 } + \frac { 8 } { 3 } x + 1$
E) $y = x ^ { 4 } + \frac { 74 } { 3 } x + 1$