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sampletest2

# sampletest2 - a ib Remember what e a ib x means In(b the...

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MAP 2302 Second Exam (Sample) Time allowed: 55 minutes 1. Solve the initial value problems (a) y + 2 y + 17 y = 0 , y (0) = 1 , y (0) = - 1 . (b) y - 4 y + 4 y = 0 , y (1) = 1 , y (1) = 1 . Click for a hint 2. Find the general solution of the equation y + 4 y = tan 2 x. Click for a hint 3. Find the general solution of the equation y - 4 y - 5 y = 2 e - x . Click for a hint 4. Given that f ( x ) = e x is a solution of the equation xy - ( x + 1) y + y = 0 , x > 0 , find a second linearly independent solution. Click for a hint

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Hints for Q1. In (a) there are complex roots
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Unformatted text preview: a + ib . Remember what e a + ib x means. In (b) the root is repeated, so e rx does not give two fundamental solutions. Back to problem 1 Hints for Q2. Use variation of parameters. Back to problem 2 Hints for Q3. Use method of undetermined coeFcients. It would be wise to solve the homogeneous equation ﬁrst. Back to problem 3 Hints for Q4. Reduction of order! Back to problem 4...
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