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Differential EquationsEasyFrobenius & Special Functions

Frobenius & Special Functions · Easy problem

The equation 2xy′′+y′+y=02xy'' + y' + y = 0 has a regular singular point at x=0x = 0. Write it as y′′+P(x)y′+Q(x)y=0y'' + P(x)y' + Q(x)y = 0 and compute p0=lim⁡x→0x P(x)p_0 = \lim_{x\to 0} x\,P(x). Express your answer as a common fraction.