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

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The Answer of Consider the second-order homogeneous differential equation 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} $

Consider the Second-Order Homogeneous Differential Equation What Is y=C1e−4t+C2e−8t y=C_{1} e^{-4 t}+C_{2} e^{-8 t} y=C1​e−4t+C2​e−8t

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