Which of the Following Is the General Solution of the Homogeneous

Multiple Choice

Which of the following is the general solution of the homogeneous second-order differential equation are arbitrary real constants.

A) $y=C\left(e^{5 t}+e^{10 t}\right)$
B) $y=C_{1} e^{-5 t}+C_{2} e^{-10 t}$
C) $y=C_{1} e^{5 t}+C_{2} e^{10 t}$
D) $y=C\left(e^{-5 t}+e^{-10 t}\right)$
E) $y=C_{1} e^{-5 t}+C_{2} e^{-10 t}+y+\left(C_{1} e^{-5 t}\right) \cdot\left(C_{2} e^{-10 t}\right)$
F) $y=\left(C_{1} e^{-5 t}\right) \cdot\left(C_{2} e^{-10 t}\right)$