Use the method of variation of parameters to solve the following third-order nonhomogeneous differential equation:
$Use the method of variation of parameters to solve the following third-order nonhomogeneous differential equation: A) y=C_{1} e^{t}+C_{2} t e^{t}+C_{3} t^{2} e^{t}-\frac{2}{5} t^{\frac{5}{2}} e^{t} B) y=C_{1} e^{t}+C_{2} t e^{t}+C_{3} t^{2} e^{t}+\frac{8}{105} t^{\frac{7}{2}} e^{t} C) y=C_{1} e^{t}+C_{2} t e^{t}+C_{3} t^{2} e^{t}+\left(\frac{1}{7} t^{\frac{7}{2}}-\frac{2}{5} t^{\frac{7}{2}}\right) e^{t} D) y=C_{1} e^{-t}+C_{2} t e^{-t}+C_{3} t^{2} e^{-t}+\frac{8}{105} t^{\frac{7}{2}} e^{t} E) y=C_{1} e^{-t}+C_{2} t e^{-t}+C_{3} t^{2} e^{-t}+\left(\frac{1}{7} t^{\frac{7}{2}}-\frac{2}{5} t^{\frac{7}{2}}\right) e^{t} F) y=C_{1} e^{-t}+C_{2} t e^{-t}+C_{3} t^{2} e^{-t}-\frac{2}{5} t^{\frac{5}{2}} e^{t}$
A)

y=C_{1} e^{t}+C_{2} t e^{t}+C_{3} t^{2} e^{t}-\frac{2}{5} t^{\frac{5}{2}} e^{t}

y=C_{1} e^{t}+C_{2} t e^{t}+C_{3} t^{2} e^{t}+\frac{8}{105} t^{\frac{7}{2}} e^{t}

y=C_{1} e^{t}+C_{2} t e^{t}+C_{3} t^{2} e^{t}+\left(\frac{1}{7} t^{\frac{7}{2}}-\frac{2}{5} t^{\frac{7}{2}}\right) e^{t}

y=C_{1} e^{-t}+C_{2} t e^{-t}+C_{3} t^{2} e^{-t}+\frac{8}{105} t^{\frac{7}{2}} e^{t}

y=C_{1} e^{-t}+C_{2} t e^{-t}+C_{3} t^{2} e^{-t}+\left(\frac{1}{7} t^{\frac{7}{2}}-\frac{2}{5} t^{\frac{7}{2}}\right) e^{t}

y=C_{1} e^{-t}+C_{2} t e^{-t}+C_{3} t^{2} e^{-t}-\frac{2}{5} t^{\frac{5}{2}} e^{t}

What Is the General Solution of the Third-Order Linear Homogeneous

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