Unformatted text preview: 3. (10 points) Consider the following diﬀerential equation ( x 2 tan x ) y = ( x 2tan x ) y. (a) (5 points) Solve the equation exactly. (b) (5 points) Using the y = e S method, derive the leading order behavior of the function near x = 0, and verify that it agrees with the exact solution. 4. (10 points) Consider the following diﬀerential equation x 4 y 00x 2 y + 1 4 y = 0 . Determine the leadingorder behavior of the two solutions to the equation near x = 0 + . 5. (10 points) Consider the following diﬀerential equation y 00 = √ xy Determine the leadingorder behavior of the two solutions to the equation near x = ∞ ....
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 Fall '08
 Young,W

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