test3spring2010

test3spring2010 - Mid Term Examination - III, Spring, 2010...

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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.) [6] 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. [8] 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. [6] 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 [10] 1 ...
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