quiz 4 - ') Show that the given set of functions is...

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Fall 2008 Math 285 Quiz 4: Oct 8 Name: If you cannot complete a problem (perhaps because you forgot a formula) but you think you know how. please describe. Correct methods will receive partial credits. 1. Find an interval containing :r = 0 for which the given initial-value problem has a unique solution. Do not try to solve the equation. (x + l)y" + y = sinx, y(O) = 1, y'(O) = 3. \.-00\( .\:OJ C\.A \. (\ uu~ \ cV\ 0\. .;~'1 C(", I .~ '-t:Y, L~ D- -\,> :< -t- \ / \ rl C \.1 _ ",. ('~ ~ " '--r- r ( 'C\ -.J V'\ I'- L7V~ LOI\ ~ I /\vOU ) (\~* 0c -t \ :to O. \.~\. ""t:.Q. .f v c\ \ . ~ ~ i-' Go f\~\v. .:'-r D.
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Unformatted text preview: ') Show that the given set of functions is linearly independent on the interval (- 00, (0). 2-L ')( 'LfiL)c 1AA &quot;\ 'X ' V1 (-c:o, CD ') \~ e. 'X I\-e '1-X-\;O(,M '&quot; ~!~,( '1 ,L~ \' 12--r o~ (--&lt;:0, DD ) 3. Find the general solution of the following second-order differential equation. &quot;-&quot;4 y-oy ~ y = . ( L l S lM-S v'V\.-r C+-::::-0 I It-.l 00 '&quot;~. 5')1\) Ll LX T C-z e-~rx (M-l~M-Cf-) ~ 0~ ~(-= e.~ 4 ~L~~'X...
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