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The respective expressions for complimentary function and particular integral part of the solution of the differential equation $$\frac{{{{\text{d}}^4}{\text{y}}}}{{{\text{d}}{{\text{x}}^4}}} + 3\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} = 108{{\text{x}}^2}$$ are

A. $$\left[ {{{\text{c}}_1} + {{\text{c}}_2}{\text{x}} + {{\text{c}}_3}\sin \sqrt {3{\text{x}}} + {{\text{c}}_4}\cos \sqrt {3{\text{x}}} } \right]{\text{ and }}\left[ {3{{\text{x}}^4} - 12{{\text{x}}^2} + {\text{c}}} \right]$$

B. $$\left[ {{{\text{c}}_2} + {{\text{c}}_3}\sin \sqrt {3{\text{x}}} + {{\text{c}}_4}\cos \sqrt {3{\text{x}}} } \right]{\text{ and }}\left[ {5{{\text{x}}^4} - 12{{\text{x}}^2} + {\text{c}}} \right]$$

C. $$\left[ {{{\text{c}}_1} + {{\text{c}}_3}\sin \sqrt {3{\text{x}}} + {{\text{c}}_4}\cos \sqrt {3{\text{x}}} } \right]{\text{ and }}\left[ {3{{\text{x}}^4} - 12{{\text{x}}^2} + {\text{c}}} \right]$$

D. $$\left[ {{{\text{c}}_1} + {{\text{c}}_2}{\text{x}} + {{\text{c}}_3}\sin \sqrt {3{\text{x}}} + {{\text{c}}_4}\cos \sqrt {3{\text{x}}} } \right]{\text{ and }}\left[ {5{{\text{x}}^4} - 12{{\text{x}}^2} + {\text{c}}} \right]$$

Answer: Option A

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