Solutions of Sample Problems for Second In-Class Exam
نویسنده
چکیده
(b) Give a general real solution of the homogeneous equation Ly = 0. Solution. A general solution is y = c1e −2t cos(3t) + c2e −2t sin(3t) + c3 cos(7t) + c4 sin(7t) + c5t cos(7t) + c6t sin(7t) + c7e 5t + c8t e 5t + c9t e + c10e −3t + c11 + c12t . The reasoning is as follows: • the single conjugate pair −2± i3 yields e cos(3t) and e sin(3t); • the double conjugate pair ±i7 yields cos(7t) , sin(7t) , t cos(7t) , and t sin(7t) ; • the triple real root 5 yields e, t e, and te; • the single real root −3 yields e; • the double real root 0 yields 1 and t.
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