Solution-8 - Sample Solutions of Assignment 8 for MATH3270A...

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Sample Solutions of Assignment 8 for MATH3270A for ODENovember 7,2013Contact Mr. XIAO Yao(yxiaoamath.cuhk.edu.hk) directly if you have any questions on thesolutionsSection 7.6In each of problems express the general solution of the given system of equations in term ofreal-valued functions. Also draw a direction field, sketch a few of the trajectories, and describethe behavior of the solutions ast→ ∞.2.x0=-11-4-1x4.x0=295-52-1x8.x0=-3021-10-2-10x
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10. Find the solution of the given initial value problem. Describe the behavior of the solution ast-→ ∞.x=-32-1-1x,x(0) =12.
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5.(a).Find the eigenvalues of two given system.(b).Choose an initial point (other that the origin) and draw the corresponding trajectory in thex1x2-plane.(c). For your trajectory in part(b) draw the graphs ofx1versus t and ofx2versus t.(d). For your trajectory in part(b) draw the graphs in three dimensionaltx1x2-space.
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