DiffEq PE1

# DiffEq PE1 - Name Section No 1 2 3 4 5 6 7 II 10 10 20 10...

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Name: Section No. 110.302 Diferential Equations December 12, 2005 Practice Final Exam One sheet (2 sides, 8 1 2 × 11) of hand-written notes may be used during this exam. No books, calculators or other materials are permitted. This exam contains 8pages and has a total of 140 points . Time: 3 hours. Please put your name on the top of each page. 1 10 2 10 3 20 4 10 5 20 6 20 7 20 II 30 Express all answers using real numbers and real functions only. (You may use complex numbers in your work, but 1 should not appear in your answer.) To receive full credit you must show all o± your work and write your answers in the indicated places. NOTE: The actual Fnal will have 140 points, but the practice has more problems.

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Name: page 2 1. (20 points) (a) Find the general solution of the equation y 0 = 3 x y . Answer: (b) For which initial conditions ( x 0 ,y 0 )istheso lut ion NOT unique? Answer: (c) Sketch the graph of the general solution for three di±erent constants (i.e. sketch three integral curves of the direction ²eld). Answer: (d) Solve for y as a function of x , y = φ ( x ), when y (0) = 1. Find the interval of existence of the solution y = φ ( x ) .
Name: page 3 2. (20 points) Solve the inhomogeneous initial value problem: y 0 y = te 2 t , y (0) = 0 ,y 0 (0) = 0 .

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DiffEq PE1 - Name Section No 1 2 3 4 5 6 7 II 10 10 20 10...

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