Classical Equations The equations in Problems 1-2 are some of the most famous differential equations in physics.5 Use d 'Alembert's reduction of order method described in Problem 75 along with the given solution y1 to find a second solution y2(t).
Be prepared for integrals that you cannot evaluate! Those answers should be left in terms of unevaluated integrals.
1. y′′ − 2ty′ + 4y = 0 , y1(t) =1− 2t2 (Hermite's Equation)
2. (1− t2) y′′ − ty′ + y = 0, y1(t) = t (Chebyshev's Equation)