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Unformatted text preview: Math 215 Final Exam. April 21st, 2007. One doublesided sheet of notes is permitted. No calculators, cellphones, books or other aids are allowed. This exam has 7 questions worth 100 points in total. Answer all questions. For each part of each question, draw a box around your final answer. 1. (30 pts) a. Solve the following system of differential equations with initial conditions. x ′ = parenleftbigg 3 2 4 1 parenrightbigg x x (0) = parenleftbigg 1 1 parenrightbigg b. y ′ = (1 + t ) e y with y (0) = 0. Find y ( t ). c. y ′′ + 4 y = t + cos 2 t with y (0) = 0 , y ′ (0) = 1. Find y ( t ). d. y ′′ + 4 y = 4 δ ( t 6) with y (0) = 0 , y ′ (0) = 1. Find y ( t ). e. Solve the following system of differential equations with initial conditions. x ′ = parenleftbigg 1 1 1 parenrightbigg x x (0) = parenleftbigg k 1 k 2 parenrightbigg 2. (10 pts) Solve the initial value problem with discontinuous forcing function g ( t )....
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This note was uploaded on 03/28/2012 for the course MATH 215 taught by Professor Keqinliu during the Spring '08 term at UBC.
 Spring '08
 KEQINLIU
 Math, Differential Equations, Equations

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