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Consider the Second-Order Homogeneous Differential Equation
What Is $y=C_{1} e^{-4 t}+C_{2} e^{-8 t}$

Question 11

Multiple Choice

Consider the second-order homogeneous differential equation $Consider the second-order homogeneous differential equation What is the general solution of this differential equation? Here, C, C<sub>1</sub> , and C<sub>2</sub> are arbitrary real constants. A) y=C_{1} e^{-4 t}+C_{2} e^{-8 t} B) y=C_{1} e^{4 t}+C_{2} e^{8 t} C) y=C_{1} e^{t}+C_{2} e^{32 t} D) y=C_{1} e^{-t}+C_{2} e^{-32 t} E) y=C_{1} e^{4 t}+C_{2} e^{-32 t}$
What is the general solution of this differential equation? Here, C, C₁ , and C₂ are arbitrary real constants.

A) $y=C_{1} e^{-4 t}+C_{2} e^{-8 t}$
B) $y=C_{1} e^{4 t}+C_{2} e^{8 t}$
C) $y=C_{1} e^{t}+C_{2} e^{32 t}$
D) $y=C_{1} e^{-t}+C_{2} e^{-32 t}$
E) $y=C_{1} e^{4 t}+C_{2} e^{-32 t}$