Consider the Homogeneous Second-Order Cauchy Euler Differential Equation

What $y=C_{1} t^{10}+C_{2} t^{6}$

Multiple Choice

Consider the homogeneous second-order Cauchy Euler differential equation

What is the general solution of this differential equation? Here, C₁ and C₂ are arbitrary real constants.

A) $y=C_{1} t^{10}+C_{2} t^{6}$
B) $y=C_{1} t^{10}+C_{2} t^{6}$ .
C) $y=C_{1} r^{10 t}+C_{2} t^{6 t}$
D) $y=C_{1} t^{10 t}+C_{2} f^{6 t}$ .
E) $y=C_{1} t^{-5}+C_{2} t^{-6}$