The answer has been given, please provide the process.question about：Nilpotent Canonical Forms 4. Classify the following operators on R4 by similarity (missing entries are 0) :(a) 0 1(b)2002 (c) 0004 03:(d)020 301 00 1-100-2 0 0(e)]"[0-1 00 0-2,-0 1004. Similar pairs are (a), (d) and (b), (c).000400

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Answered: 4. Classify the following operators on…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Problem 1RQ

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Solve second order ode using lie symmetry condition and explain steps clearly in detail. ( ie canonical variable,lie point symmetries,r , s etc ) yy'' - y'^2 = 3y^2 lny( Full calculation and answer ). I have the infinitesimal generator X = d/dx. Can I solve it, find general solution, by using lie symmetry condition, canonical coordinates(r and s), canonical variables. I have to follow these steps to solve this question: 1) find the lie symmetries, 2) find canonical coordinates, 3) substituting canonical variables, 4) solving ODE in new coordinates, 5) Returning to original coordinates- general solution. Can u help me follow these steps in order to answer the question above please?’—> that was the original question. I got y'y'' + yy''' - 2y'y'' = 3y + 6ylny from subbing in X= d/dx, differentiating. I then simplified this equation to: yy''' - y'y'' = 3y + 6ylny, simplifying the original equation. I then introduce canonical coordinates r = y’ and s = y” and substitute that into…
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4. Classify the following operators on R4 by similarity (missing entries are 0): (b) 200 2 (c) 0 NEN 00 -2 (e) 0 0 0 100 0 (a) 0 1 02 0 3 (d) 0 1 0 0 1 0 -1 -1 0 - 4. Similar pairs are (a), (d) and (b), (c). 40 04 00