Differential Equations Exam Review (4 of 6) - Review 3 L15-L21 1 Using the mass-spring analogy predict the character(justify your answer of the solution

Differential Equations Exam Review (4 of 6) - Review 3...

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1 Review 3: L15-L21 1. Using the mass-spring analogy, predict the character (justify your answer) of the solution: overdamped, critically damped, underdamped or oscillatory motion, simple harmonic oscillation, exponentially growing, exponentially increasing/decreasing motion (indicate the bounded solution), and exponentially growing sinusoid. Determine the end behavior, ( )limty t→∞, if the limit exists. Then confirm your prediction by actually solving the problem. Graph the solution. (a) 560yyy′′++=(0)1y=, (0)1y=(b) 8160yyy′′++=; (0)1y= −, (0)6y=(c) 40yy′′+=(0)1y=, (0)23y= −(d) 230yyy′′++=(0)1y=, (0)1y=(e) 450yyy′′+=(0)1y= −, (0)2y=(f) 60yyy′′+=; (0)1y=, ( )00yv=2. Use the method of undetermined coefficients to find a particular solution to the nonhomogeneous equation. (a) 1yy′′=(b) 1yy′′ −=(c) 225tyyye′′++=(d) 25tyyye′′++=(e) 3 cos2yytt′′ +=(f) 3cosyyt′′ +=3. Use the method of undetermined coefficients to find the form of a particular solution to 2455costyytet′′+=4. Find a general solution to the equation 22cos2sin 2ttyyyetet′′+=. Please go over the following steps: 1)Find the general solution to the homogeneous equation, ( )hyt. 2)Find a particular solution by using method of undetermined coefficients, ( )pyt. 3)Give the general solution to the equation by using the superposition principle. 5. Solve the initial value problem: 2244,(0)0,(0)1ttyyyteeyy′′+=+==.

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