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Find general solution of y" + 2y' + y = 2e^-t

Answer: c1e^-t + c2t^-t + t^2e^-t

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Deanna L. | Electrical engineering major and music lover with MIT degreeElectrical engineering major and music l...
4.9 4.9 (129 lesson ratings) (129)
This is second order diff equatin which means if you break it down in the form of ay'' + by' + cy  you get general solutions of -b/2a or -1. (the b^2-4ac terms disappear from the quadratic formula). That means that by definition the general solution is C1e^-t + c2te^-t. The double integral of 2e^-t is t^2e^-t (first integral is 2te^-t).
Add those terms together for the total solution. Hope that helps!