Final2005summer

# Final2005summer - Final Examination Dierential...

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Final Examination Diﬀerential Equations/Linear Algebra MTH 2201 07/08/2005 Time: 2 hours Max.Credit: 50 Answer all the questions. Make your asnwers precise and write legibly. Calculators are NOT allowed. 1. Determine whether x = 0 is a ordinary point/singular point for the following diﬀerential equations: (i) The Legendre Equation (1 - x 2 ) y ±± - 2 xy ± + y =0 . (ii) 2 x 2 y ±± - xy ± +(1+ x ) y . [4] 2. Consider the matrix A = ± 2 - 1 32 ² . (a) Find the eigen values and eigen vectors of A . [4] (b) Find the fundamental matrix Φ( t ) of the diﬀerential system x ± =Ax . [3] (c) Find the inverse Φ - 1 ( t ) of the fundamental matrix Φ( t ) . [3] (d) Find a particular solution of the nonhomogeneous system x ± = A x + g(t) where g ( t )= ± e t t ² . [4] 3. If ± 1 i ² is an eigenvector for a matrix A, corresponding to an eigenvalue λ = - 1 2 + i, give two linearly independent real valued solutions of the sytem of

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## This note was uploaded on 03/02/2011 for the course MATH 1101 taught by Professor Tenali during the Spring '11 term at FIT.

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Final2005summer - Final Examination Dierential...

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