PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Ordinary differential equations · Ordinary differential equations
Conditions of Validity, Ch Series solutions, singular points and where the special functions come from
Problem
The equation 2x2y′′+3xy′−(1+x2)y=0 has a regular singular point at x=0.
((a)) Find the indicial equation and its two roots.
((b)) State which of the three exponent-difference cases applies.
((c)) Construct the Frobenius series y=xs∑k=0∞akxk for the larger root, with a0=1, and give the coefficients a2 and a4 (odd coefficients vanish).