ENGIN 117 Study Guide - Midterm Guide: Partial Fraction Decomposition
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If so, what would you take as a form yp(x) for the particular response? (hint: write out cosh in terms of elementary exponential functions. ) Since cosh x = 1/2(ex + e x), the forcing term has a com- ponent which is part of the homogeneous response, on its double root. Therefore the particular response is of the form ax2ex + be x. (d) solve for for yp(x). 1 yh(0) = 1 and y is satis ed when c = 1 and d = 1, thus: h(0) = 0. Since yh(x) = cex + dxex, this y(x) = 2x2ex + e x ex + xex: a system of odes is written in the form dy(t) dt. Then y(t) = y1e 3t + y2e t (b) now solve for the two vectors y1 and y2 by using the eigenvalues calculated in part (a). For = 3, we seek the solution to. 0 # which is satis ed for x2 # = "
