test 2 spring 06 - Using Euler's method with step size h...

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.r Name: Recitation: Math 240 t'") Exam 'X,' v March 14, 2006 Closed book. You may use a calculator and one 8 ~ x 11" sheet of handwritten notes (both sides). You must show your work to receive full credit. Write solutions in explicit form if possible. All problems have a solution that can be found using the techniques of this class. Problems that ask for answers in paragraph form will be graded on both content and clarity. Points may be deducted for errors in spelling and grammar. Pledge: On my honor, as a student, I have neither given nor received unauthorized aid on this examination: (signature) (date) Problem Score 1 2 3 4 5 6 7 8 Total
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Name: 1. Find all solutions to ~ +6: +10y=cos(x).
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Name: 2. Solve the initial value problem d2 d --{-+ 72+ 10y = 0, y(O) =1, y'(O) = 1. dx dx
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Name: 3. Find y(l) where y(x) is the solution to the initial value problem, d2 d -? +22 +5 y = 13e2X,y(O) =2, y'(O) =1. dx dx
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Name: 4. Rewrite cos(2x)-2sin(2x) in the form Acos(2x+~).
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Name: 5.
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Unformatted text preview: Using Euler's method with step size h = .1, approximate x(.2) if d2x dX ,-+-+x=t X ( O ) =3 xfO ) =-2 dt2 dt ' , \ . Name: 6. Match the following differential equationswith the graphs of one of their solutions. (a) x"+36x = 5cos(6t) (b) x"+36x=30cos(5t) (c) x"+.55x'+36x = 30cos(5t) xmax 7 xmln [7 xmax 7 xmln ~-7 xmax 7 xmin te=J ~ Imln 18.84 Imax L... Imin 18.84 L--tmax fa I Imin 18.84 Imax Equation Equation Equation Name: 7. A mass is attached to an undamped spring, causing it to stretch 8cm. The mass is then pulled down an additional distance and released. How long will it take the mass to return to the point at which it was released? Use g = 981cm/sec2.Yes, you do have enough information to solve this problem. Name: 8. Find a differential equation whose general solution is y = e-x + cte-Xsin(2x) + c2e-x cos(2x). Name:...
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This note was uploaded on 04/07/2008 for the course MATH 240 taught by Professor Yetter during the Fall '07 term at Kansas State University.

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test 2 spring 06 - Using Euler's method with step size h...

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