Final2010spring

Final2010spring - Final Examination - Spring, 2010....

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Unformatted text preview: Final Examination - Spring, 2010. Differential Equations/Linear Algebra MTH 2201 5/3/2010 Time: 2 hours Max.Credit: 60 Answer as many questions as you can. Make your answers precise and write legibly. Calculators are NOT allowed. 1. Find the value of b for which the the first order ODE ( xy 2 + bx 2 y ) dx + ( x + y ) x 2 dy = 0 is exact and solve it using that value of b . [6] 2. Given that y 1 ( t ) = 1 is a solution of the ODE, (1- t 2 ) y 00 + 2 ty = 0, Use the method of reduction of order and find a second solution y 2 ( t ) such that y 1 , y 2 are linearly independent. [5] 3. (a) Determine the general solution of the homogeneous differential equation y 000- 4 y 00 + 4 y = 0. [4] (b) Use the method of undetermined coefficients method to determine the form of a particular solution for y 000- 4 y 00 + 4 y = 5 x 2- 6 x + 4 x 2 e 2 x + 3 e 5 x . [5] 4. (a) Find the general solution of the Cauchy Euler equation t 2 y 00 + ty = 0 . [5] (b) Use method of variation of parameters to find a particular solution of the ODE...
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Final2010spring - Final Examination - Spring, 2010....

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