# Lecture Notes for MATH 2214 - Intro Diff Equations with Glynn at Virginia Tech (VT)

## Notes Information

 Material Type: Note Professor: Glynn Class: MATH 2214 - Intro Diff Equations Subject: Mathematics University: Virginia Polytechnic Institute And State University Term: Spring 2006 Keywords: CalculatorsEigenvaluesOrder EquationsEigenvectorEigenvectorsMultiplicityValue ProblemHigher OrderInitial ValueOrder Linear    ## Sample Document Text

o 0~,���� .. ' \ 'f" ~- 0(': 0 --!" \F" .. �� � " ~~ Math 2214 Review Problems for Exam 3, Spring 2006 Show all work. No credit will be given for unsupported answers. Circle your answers. No calculators allowed. 1. Find the general solution of y(4) + 2y"' + 2y" + 2y'+'1 = O. (Hint: (.>-2 + 1) is a factor of the characteristic polynomiaL) 2. Rewrite (t 2 +l)ylll + (sin t)y" - (et)y = t 2 as a. system of first order equations y'(t) = P(t)y(t) + g(t). Identify the matrix function P(t) and the vectol: functions g(t) and y(t) . -------- 3. Compute the vVronskian of the solutions Yl (t) = ( ~ ) e- 5t of the system of differential equations y' = P(t)y. Could {ydt), Y2(t), Y3(t)} be a funda mental set of solutions for such a system of differential equations where P(t) is a three by three matrix with entries that are continuous on (-00, oo)? 4. Find the general solu tion of ( 1 0 0) y' = 2 2 0 y. 113 5. Find the general solution of y' = Ay if A is a (2 X 2) const...

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