Unformatted text preview: di f erent cases for the eigenvalue problem): ∂ u ∂ t = ∂ 2 u ∂ x 2 , < x < π , t > BC : u (0 , t ) = 0 = u ( π , t ) IC : u ( x, 0) = 2 cos x sin x [20 marks] 3. Consider the second order di f erential equation: Ly = 2 xy 00 + (1 + x ) y + y = 0 (1) (a) Classify the points x ≥ (do not include the point at in f nity) as ordinary points, regular singular points, or irregular singular points. [5 marks] (b) Use the appropriate series expansion about the point x = 0 to determine two independent solutions to (1). You only need to determine the f rst three non-zero terms in each case. [35 marks] 1...
View Full Document
This note was uploaded on 04/06/2012 for the course MATH 257 taught by Professor Peirce during the Fall '08 term at UBC.
- Fall '08