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Find the power series solution of the equation : d²y dx2 about its singular point. x2 dy + 4x dx + (x² + 2) y = 0

Find the power series solution of the equation : d²y dx2 about its singular point. x2 dy + 4x dx + (x² + 2) y = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the power series solution of the equation : dy dx x2 d²y dx² about its singular point. + 4x + (x² + 2) y = 0 Construct Green's function for following boundary value problem : d²y dx² with y (0) - y (1) = 0. Find the solution of V2u = 0 in R subject to R triangle 0≤x≤ 1, 0 ≤ y ≤ 1, 0 ≤ x + y ≤ 1 and u (x, y) = x² - y² on the boundary of the triangle. Assume h = 1 4 +9y = 0 and use five-point formula. Show that the method : 1 4 Yi+1=YiYi-1 + 3 2h Yi-1+Yi+1 3 3 the is absolutely stable when applied to the equation y'= Ay, λ < 0.
Transcribed Image Text:Find the power series solution of the equation : dy dx x2 d²y dx² about its singular point. + 4x + (x² + 2) y = 0 Construct Green's function for following boundary value problem : d²y dx² with y (0) - y (1) = 0. Find the solution of V2u = 0 in R subject to R triangle 0≤x≤ 1, 0 ≤ y ≤ 1, 0 ≤ x + y ≤ 1 and u (x, y) = x² - y² on the boundary of the triangle. Assume h = 1 4 +9y = 0 and use five-point formula. Show that the method : 1 4 Yi+1=YiYi-1 + 3 2h Yi-1+Yi+1 3 3 the is absolutely stable when applied to the equation y'= Ay, λ < 0.
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