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

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Review 3: L15-L211. Using the mass-spring analogy, predict the character (justify your answer) of thesolution: overdamped, critically damped, underdamped or oscillatory motion, simpleharmonic oscillation, exponentially growing, exponentially increasing/decreasing motion(indicate the bounded solution), and exponentially growing sinusoid. Determine the endbehavior,( )limty t, if the limit exists. Then confirm your prediction by actually solvingthe problem. Graph the solution.=====
12. Use the method of undetermined coefficients to find a particular solution to thenonhomogeneous 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 to2455costyytet′′+=4. Find a general solution to the equation22cos2sin 2ttyyyetet′′+=.======Please go over the following steps:1)Find the general solution to the homogeneous equation,( )hyt2)Find a particular solution by using method of undetermined coefficients,( )pyt3)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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