Cauchy-Euler equations
General · Mathematics
Study notes
Q: Solve x²y''-3xy'+4y = 0. Try y = x^m: y' = mx^(m-1), y'' = m(m-1)x^(m-2). x²·m(m-1)x^(m-2) - 3x·mx^(m-1) + 4x^m = 0. [m(m-1)-3m+4]x^m = 0: m²-4m+4 = (m-2)² = 0. m = 2 (double!): y = (A+B ln x)x²! (Repeated root: ln x factor!)