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practice exam I

# practice exam I - Practice Exam 1 Math 244 Diff Eq.s Prof...

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Practice Exam 1, 2/15/2012, Math 244 Diff. Eq.s, Prof. Tumulka 1 2 3 4 5 6 7 8 9 10 11 Σ Name: Given formula: The general solution of the first order linear ODE y 0 + p ( t ) y = g ( t ) is y ( t ) = 1 μ ( t ) Z μ ( t ) g ( t ) dt + c , μ ( t ) = e R p ( t ) dt Calculators, books and notes are not allowed. Good luck! 1) [worth 4 points out of 100] True or false? The global truncation error in the Runge– Kutta method has an upper bound proportional to (Δ t ) 5 . 2) [4 points] In which case does one say that the DE y 00 + p ( t ) y 0 + q ( t ) y = g ( t ) is homogeneous? 3) [7 points] a) What does the “superposition principle” say? b) To which of the following DEs does it apply? (i) y 00 - 4 y = sin t yes no (ii) y 00 + (sin t ) y 0 - 4 y = 0 yes no (iii) y 00 - 4 y 0 + sin y = 0 yes no 4) [5 points] Determine the longest interval in which the IVP ( t - 1) y 00 - 3 ty 0 +4 y = sin t , y ( - 2) = 2, y 0 ( - 2) = 1 is certain to have a unique solution. Do not attempt to find the solution. 1

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