Review for exam 4Thursday, October 25 , 2018Here is a list of topics that you should well understand for the exam:•Reduction of Order•Variation of Parameters•Heaviside function•Calculus of discontinuous functions•Laplace transform rules with Heaviside functions•Solve differential equations with discontinuous input functions•Impulse functions: The Dirac delta function,δc•Laplace transform rules with the Dirac delta function•Solve differential equation with impulse functions•Mixing problems with discontinuous or impulse inputs•Systems of differential equations•The matrix exponential,eAt•The Laplace transform ofeAtand its inversion•Fulmer’s methodBelow are typical problems from previous exams. I am not writing up solutionsas there are plenty of solutions to similar problems in the solution manual.Problem1.Solve the following differential equations:1.t2y′′+ty′+ 4y= 02. 2t2y′′-5ty′+ 3y= 03.t2y′′+ 7ty′+ 9y= 04.t2y′′+ 3ty′+y= 05.t2y′′+ty′+ 4y= 0Math 20701
Review for exam 4Thursday, October 25 , 2018
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Calculus, Dirac delta function, Use variation of parameters, t2 Y