# Week2_Old test - Solve the following DE problem for y ( t...

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Mech 221 Math Problems from Old Tests, Week #2 Brian Wetton September 28, 2010 Notes: This contains all questions on Mech 221 tests and exams from 2006- 09 on the material on direction ﬁelds and ﬁrst order linear diﬀerential equations. Some of this material may appear on your tests #3 or #4 this year, depending on how far I get in the lectures. Also, some of the numerical methods material covered in the Old Test Problems last week may appear on your test #2 this year. Remember that, as discussed in class, no solutions will be provided for these questions . Short Question, Exam, 2008: Consider the following linear, scalar diﬀer- ential equation for x ( t ): dx dt + x t = t 2 (a) [2 marks] What is the integrating factor for this equation? (b) [3] Multiply the equation by the integrating factor and solve for x ( t ) with initial conditions x (1) = 0. Short Question, Test #2, 2007: Find the solution y ( t ) of the diﬀerential equation y 0 + t 3 y = 0 with initial conditions y (1) = 5. Short Question, Test #4, 2006:

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Unformatted text preview: Solve the following DE problem for y ( t ): dy dt + y = t with y (0) = 1 Short Question, Test #2, 2006: Solve the following DE problem for y ( t ): dy dt + (sin t ) y = 0 with y (0) = 1 1 Short Question, Test #2, 2009: The function y ( t ) solves the diﬀerential equation dy dt + 3 y = 0 (a) [3 marks] What is the general solution to this DE? (b) [2] If y (1) = 2 what is the solution y ( t )? Short Question, test #4, 2009: Consider the following linear diﬀerential equation for y ( t ): dy dt + ty = t (a) [2 marks] What is the integrating factor for this equation? (b) [3] Multiply the equation by the integrating factor and solve for the general solution y ( t ). 2 Short Question, Exam, 2007: Match the four direction ﬁelds and solu-tions plotted below ( y versus t ) to the four diﬀerential equations below: (a) y = y cos t 1+2 y 2 (b) y = t 2 ( y-1)( y-2) (c) y = t-3 y (d) y = y 2-t 3...
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## This note was uploaded on 10/26/2010 for the course ENGINEERIN MECH221 taught by Professor Wetton during the Spring '10 term at The University of British Columbia.

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Week2_Old test - Solve the following DE problem for y ( t...

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