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Unformatted text preview: per minute, and the wellstirred solution runs out at 40 liters per minute. Write down 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 + 12 y + 36 y = 0 , y (0) = 3 , y (0) = 2 7. (12 points) Find the general solution of the following dierential equations. 9 y 00 + 6 y + 37 y = 0 8. (12 points) Suppose y ( t ) satises y = 2 t 2 + y 2 and y (1) = 1. 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 ( x5)( x + 4) 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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 Fall '10
 GODDARD
 Differential Equations, Equations

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