Question

Solve for the general solution on question number 6.

9 5 -1) Cion of the given initial value problem. 4. X = -3 0 6. x = 1 -1 0x -2 - 1 4 RC; si (b) solution (c) (d) 13. 0 are l

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Answer #1

X - 3 0 2 X -2 O Let A -3 0 2 -1 0 - 2 -1 o The characteustic equation A-AID -X-3 2 -1- O -2 -1 - > -43-412-71-6=0 The rootsCase I iet be the eigen vector mz т3 corresponding -1 2 =) 1 2 | 2 88 :) mi - O m3 =) 20 mi 2 m3 m2t2m3=0 Here mz is free, le2 - 2 e 5 i hi nz 2 ng - 2-25 o nit 2 - 2 + 2 i ng 2 - 0 +-( Here n3 = 1 n2t-1 -2-252 i ng is free, det -1 trz 3 2+ i 3 nz -흐 -2-5) 2. -24252) 123 다. - 2 if 2-S e + 2 22 Heue is faree, ) Pro 1F NET p3 let P3계 P = 2-Jzi 3 3. be 2 3 1. 3 3 bi P3 Hence

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