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Exam 2 nice - a rt 1 Problem 4(20 points Use the method of...

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M427K (Unique number 58610 ) In class exam Nov 8 2005 Problem 1 (20 points) Solve the initial value prob l em y’’ – 6y’ + 9y = 0; y(0) = 1; y’(0) = 0 using Laplace transform. Partial credit will be assigned by sol v i ng the problem by any other method. Al so , extra credit will be assigned by solvin g i t b y Laplac e ' s method and another method . Problem 2 (20 points) For each of the following equations find the general solution. (1) y’ = y 2 (1-y) (2) y' + ( 1/t)y = t 3 Problem 3 (20 points) 1) Use the method of undetermined coefficients to find a particular solution of the equation y (3) - y = 2e t 2) Write the general solution of the equation in p
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Unformatted text preview: a rt 1 Problem 4 (20 points) Use the method of variation of parameters to find the general solution of the equation t 2 y" - 2y = 3t 2- 1 knowing that Y 1 (t) = t 2 , Y 2 (t) = t-1 are solutions of the homogeneous equation . Problem 5 (20 points) A mass of 100g stretches a spring 5cm when you hang the mass from the spring. Suppose that the ma s s is also attached to a damper of constant 400dyna - sec/cm. If the mass is pulled 2cm and then released without initial velocity, find its position as a function of time. (Use the acceleration of gravity 10m/s 2 .)...
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