# Past Exam for MATH 2214 - Intro Diff Equations with Linnell at Virginia Tech (VT)

## Exam Information

 Material Type: Exam 3 Professor: Linnell Class: MATH 2214 - Intro Diff Equations Subject: Mathematics University: Virginia Polytechnic Institute And State University Term: Fall 2006 Keywords: Constant VectorThe IndependentIndependentGeneral SolutionEigenvectorImaginary PartsOriginal EquationGeneralizedEigenvectorsHomogeneous   ## Sample Document Text

Math 2214 Friday, November 10 Third Test. Answer All Problems. Please Give Explanations For Your Answers 1. Find the general solution of the differential equation y (4) +2y primeprime +y = 0. (10 points) 2. Write the linear differential equation y primeprime +ty prime +t 2 y = t 3 in the form y prime = P(t)y+g(t), where P isa2�2 matrix. Identify the matrix function P(t) and the vector function g(t). (10 points) 3. Find the general solution of the system of differential equations x prime = 2x?y, y prime = x. (15 points) 4. Let A = parenleftbigg 1 ?1 2 ?1 parenrightbigg and g = parenleftbigg e t 0 parenrightbigg . Find the general solution of the system of differen- tial equations y prime = Ay+g by the method of undetermined coefficients. (15 points) Math 2214 Friday, November 10 Solutions to Third Test 1. The characteristic equation is r 4 +2r 2 +1 = 0, which is (r 2 +1) 2 = 0. Since the roots of r 2 +1 are �i, we see that the roots of (r 2 +1) 2 are �...

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