Answer Happy

Given Problem and Notes. THANKS IN ADVANCE UPVOTE
ulz on Hermite solution a-2 are ver The negative sign is left out - The negative sens absorbed 10 The solution of Hermite's equation y - 2xy +2= ) {5:22-2) = CER + + + -) (22+19 When or positive integer a) If = even integer, the coefficient of a terminates each term for k **2) will be rero b) in odd integet the coefficient of a terminates, each term for k 2+1) will be zero In both cases one of the solutions will be a polynomial (not an infinite series). Hermite's equation of degree or positive integer will always have a polynomial solution (with a finite number of terms). 22- 2(-1)-2-0-02) 2) 2) >> -- 21-1--2--22) UP 2- »---, Odd or even series PROBLEM: xy" - 2x²y' + 38 xy = 0 The Hermite polynomial From the solution y as given the Hermite polynomial ) can be obtained. (1) - H, (x) - Σκο 2-)! where greatest eerst y = H.(x) is a solution of Hermite's equation (buto a complete solution) - Ex. y" - 2xy + 14 = 0 21 - 14 = 7 Herre equation of depree 7 One solution is y=cH,(x) Complete solution: y = H.(x) + (appropriate series