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Differential EquationsEasyFrobenius & Special Functions

Frobenius & Special Functions · Easy problem

The Cauchy–Euler equation x2y′′−xy′+5y=0x^2y'' - xy' + 5y = 0 has real solutions of the form xαcos⁡(βln⁡x)x^{\alpha}\cos(\beta\ln x) and xαsin⁡(βln⁡x)x^{\alpha}\sin(\beta\ln x) with β>0\beta > 0. Compute α+β\alpha + \beta.