Frobenius method
General · Mathematics
Study notes
Q: Solve 2xy''+y'+xy = 0 by Frobenius about 0. Regular singular (x=0)! Try y = x^rΣaₙxⁿ. Indicial: from lowest power: 2r(r-1)+r = r(2r-1) = 0: r = 0, 1/2. r = 0: recurrence gives aₙ; r = 1/2: second solution! Two solutions (r differ by 1/2, non-integer: no log!)! (Frobenius handles singular points!)