The differential equation y" - 2xy' + 2ay = 0 is known as Hermite's equation of order a
Chapter 5, Problem 27(choose chapter or problem)
The differential equation y" - 2xy' + 2ay = 0 is known as Hermite's equation of order a after the French mathematician Charles Hermite (1822-1901 ). Show that the general solution of the equation is y(x) = c0 y1(x) + c1y2(x), where 00 2ka(a - 2)00(a - 2k + 2) Y1(X) = 1 + :L(-l)k x 2 k k=l (2k)! 00 2k(a - l)(a - 3) .. (a - 2k + 1) Y2(x) = x + :L
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