MTH 286 Final: MTH 286 Cleveland State pracFinalsol
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Note that this list of questions is not exhaustive. You should also be prepared to answer questions such as those on test 1, test 2, the make up test for test 2, inclass quizzes, and homework assignments. A copy of p. 557 from the text will be provided with the nal exam. Write your name on the back of your test. Where possible test your solutions: solve the initial value problem of the di erential equation: dy dt. Solution: this is a rst order linear di erential equation, so we employ the method of integrating factors. First we rearrange the equation to put the unknown function and its derivatives on the left-hand-side, Multiply both sides by the integrating factor dy dt . Integrating both sides gives e(cid:1) ( (2t)/(1+t2))dt = e ln(1+t2) = We use a trigonometric substitution to evaluate the right-hand-side. Let t = tan , then dt = sec2 d . (cid:2)
