Which of the following statement(s) are true for the given differential equation? x²y" – 5xy' + 13y = 30x? Lütfen bir ya da daha fazlasını seçin: p2 – 5r + 13 = 0 is a characteristic polynomial of the...

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Extracted text: Which of the following statement(s) are true for the given differential equation? x²y" – 5xy' + 13y = 30x? Lütfen bir ya da daha fazlasını seçin: p2 – 5r + 13 = 0 is a characteristic polynomial of the differential equation. Its homogeneous solution is y# = e" (C1 cos (2æ) + C2 sin (2x)) for arbitrary constants C1 and C2. To find particular solution, the variation of parameters can be used. It is a second order nonhomogeneous Cauchy-Euler differential equation. Its characteristic polynomial has 3+ 2i and 3 – 2i complex roots. - d'y Using t = In x , we get dt2 6 + 13y = 30eª. - dt