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Unformatted text preview: di f erent cases for the eigenvalue problem): u t = 2 u x 2 , < x < , t > BC : u (0 , t ) x = 0 = u ( , t ) x IC : u ( x, 0) = 2 sin 2 ( x ) [20 marks] 3. Consider the second order di f erential equation: Ly = 2 x 2 y 00 + 3 xy (1 + x 2 ) 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...
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- Fall '08