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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:
  • Calculators
  • Eigenvalues
  • Order Equations
  • Eigenvector
  • Eigenvectors
  • Multiplicity
  • Value Problem
  • Higher Order
  • Initial Value
  • Order Linear
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o 0~,ииии .. ' \ 'f" ~- 0(': 0 --!" \F" .. ии и " ~~ 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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