Unformatted text preview: y 1 = x 2 and y 2 = x 2 (ln x ) are solutions to x 2 y 003 xy +4 y = 0, ﬁnd the general solution to x 2 y 003 xy + 4 y = x 2 . (You may assume that we work in x > 0.) 5. Using an integration factor, solve the equation ( y + xy ) dx + xdy = 0. 6. Use the Laplace transform to solve the initial value problem y 00 + y = ( 1 , ≤ t < π/ 2; , t ≥ π/ 2; y (0) = 0 ,y (0) = 1 . 7. Prove that L{ f ( t ) } = s L{ f ( t ) } f (0). 1...
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This note was uploaded on 01/17/2010 for the course MATH 108 taught by Professor Trangenstein during the Fall '07 term at Duke.
 Fall '07
 Trangenstein
 Math

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