Show that the solutions of the differential equation y" +py' + qy=0, where y(x) is the unknown function and p, q are som

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Show That The Solutions Of The Differential Equation Y Py Qy 0 Where Y X Is The Unknown Function And P Q Are Som 1 (16.86 KiB) Viewed 35 times

Show that the solutions of the differential equation y" +py' + qy=0, where y(x) is the unknown function and p, q are some real constants, form a two-dimensional vector space. [Hint. Use the fact from MTHS130 that for any pair of initial conditions y(0) = yo. y'(0) = y₁ there exists exactly one solution.] Let A be a 2 x 2 matrix. Prove that the matrices {A, A2, A³, A4, A5} are linearly dependent.