# Past Exam for MATH 211 - ORDINARY DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA at Rice (Rice)

## Exam Information

 Material Type: Final Professor: Staff Class: MATH 211 - ORDINARY DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA Subject: Mathematics University: Rice University Term: Fall 2000 Keywords: CircumstancesPopulationsThe IndependentCalculatorsAvailabilityQualitativeSpring ConstantValue ProblemFundamental SetSubstitution

## Sample Document Text

Math 211 Final Exam December 3, 2000 Instructions: This is a closed book, three hour exam. Calculators are not allowed. Please give reasons for all of your answers. There is a short table of integrals on the last page which might be of help to you. Print your name: Print your section number: Write out and sign the pledge: 1. (8 points) Find the solution to the initial value problem dy dt + y tan t = cos t · sin t with y(0) = 0. What is the interval of existence of the solution? 2. (8 points) Solve the initial value problem x primeprime + 6x prime + 13x = 0 with x(0) = 2,x prime (0) =?2. 3. (8 points) Consider the equation y prime = (y 2 + 2y)(1 + y) 2 . a) Find and analyze all equilibrium points. b) Provide a sketch showing the qualitative behavior of all solutions. 4. (10 points) Consider the system x prime = x(1 ? y) y prime = x 2 ? y. a) Find and analyze the equilibrium points. b) Sketch the nullclines. On your sketch indicate the direction of the vector field alon...

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