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{"ops":[{"insert":"1. The eigenfunction equation X00 = -\u03bbX is regular since s(x)\u03c1(x) = 1 , 0 for all x.\n2. Bessel\u2019s equation is regular for x 2 [1; 2].\n3. Bessel\u2019s equation is singular for x 2 [0; 1].\n1. Solve the Sturm-Liouville equation X00 = -\u03bbX on [0; \u03c0] with data X(0) = 0 and X(\u03c0) = 0,\nAns: eigenfunction X(x) = sin(nx) eigenvalue \u03bb = n2, for any positive integer n.\n2. Solve the Sturm-Liouville equation X00 = -\u03bbX on [0; L] with data X(0) = 0 and X0(L)+hX(L) =\n0.\n( Ans: eigenfunction X(x) = sinx p\u03bb\u0001 eigenvalue \u03bb given by a positive solution of the transcendental equation p\u03bb + h tanL p\u03bb\u0001 = 0.\n"}]}
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