The second-order homogeneous linear differential equation whose characteristic equation has roots − 3 8 + 1 4 𝑖 and − 3 8 − 1 4 𝑖 is: Hint: A quadratic equation whose roots are 𝛼 and 𝛽 is:   𝑋 2 − ( 𝛼 + 𝛽 ) 𝑋 + 𝛼 𝛽 = 0 .单项选择题

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Question25 Consider the homogeneous linear second-order differential equation with constant coefficients:[math]where [math], [math], and [math] are constants and [math]. Which of the following statements is true about the set of all solutions to this differential equation?Select one alternative: The set of all solutions does not form a vector space because the differential equation involves second derivatives. The set of all solutions does not form a vector space because constant functions are never solutions. The set of all solutions forms a vector space only if [math] and [math]. The set of all solutions forms a vector space because sums and scalar multiples of solutions are also solutions. ResetMaximum marks: 1 Flag question undefined

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