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MATH201 Midterm 2011 F Solution

MATH201 Midterm 2011 F Solution - MATHEMATICS 201 MIDTERM...

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MATHEMATICS 201 MIDTERM EXAMINATION 29 October 2011 90 minutes Please print clearly in the table below: FIRST NAME SURNAME STUDENT ID Indicate your section in the table below: X Section Instructor EA1 TB Moodie EB1 E Woolgar EC1 V Bouchard This exam has 9 pages including this cover and a table of Laplace transforms. Please ensure that you have all pages, and write your name at the top of each page. The exam will be marked out of 50 points . There are 6 questions. The points for each question part are indicated in the margin, as well as on the last page. Answers must be accompanied by adequate justification. If you run out of space, use the back of any page for answers, as needed. Clearly direct the marker to answers that you provide on the back of a page. No calculators, notes, texts, or any other aids are allowed. 1
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1. Find the general solution of the given differential equation. You may leave the solution in implicit form if you wish. (a) ( y + x sin x ) dx + ( e y + x ) dy = 0 [6] Solution: ∂F ∂x = ( y + x sin x ) F = xy - x cos x + sin x + g ( y ) ∂F ∂y = x + g 0 ( y ) g 0 ( y ) = e y g ( y ) = e y Thus, the solution of the problem can be written (in implicit form) as xy - x cos x + sin x + e y = C = const.
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