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Unformatted text preview: BUT DO NOT SOLVE the initial value problem whose solution gives the amount of dye in the tank t minutes after the process starts. 6. (12 points) Solve the following initial value problem. y 00 + 10 y + 25 y = 0 , y (0) = 4 , y (0) = 5 7. (12 points) Find the general solution of the following dierential equations. 4 y 00 + 4 y + 37 y = 0 8. (12 points) Suppose y ( t ) satises y = 3 t 2 + y 2 and y (1) = 0. Use Eulers Method with step size h = t = 0 . 1 to approximate y (1 . 2). DO NOT ROUND OFF! 9. (8 points) Determine the longest interval in which the dierential equation ( x + 5)( x4) y 00 + 3 xy + (ln(  x  )) y = 0 has a unique twice dierentiable solution satisfying the given initial condition. (a) y (1) = y (1) = 3 (b) y (6) = y (6) = 18...
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This note was uploaded on 01/27/2012 for the course MATH 427 k taught by Professor Goddard during the Fall '10 term at University of Texas at Austin.
 Fall '10
 GODDARD
 Differential Equations, Equations

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