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Unformatted text preview: Mid Term Examination - III, Spring, 2010 Diﬀerential Equations/Linear Algebra MTH 2201 Time: 60 min 04/15/2010 Max.Credit: 30 Answer all the questions. Make your answers precise and write legibly. Calculators are NOT allowed. 1. Use the method of undetermined coeﬃcients and write an expression for the particular solution of the diﬀerential equation d5 y d3 dy + 2 dxy + dx = x2 + 2 sin x − cos x. (Do NOT solve for the undetermined 3 dx5 coeﬃcients.) 
4 2. Make the diﬀerential equation xy − x y = x4 a Cauchy Euler equation and ﬁnd the general solution, using method of variation of parameters.  3. Find the general solution of a 9th order homogeneous diﬀerential equation whose auxiliary equations has the roots √ √ 1 + 2, 1 − 2, −1 ± 2i, −1 ± 2i, 3, 3, 3.  4. Find a fundamental matrix and the general solution of the system of diﬀerential equations: dx =x dt dy = 2x + 2y − z dt dz =y dt  1 ...
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