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(t) 18. Use Laplace transform to solve the following IVPs for Зл — За2 + 2, (0) — 1 (a) , — — 6х1 — t, x2(0)=please be as specific as possible and show how to multiply the matrices together. Thank you

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Apply Laplace Transform L[x]) = 3 L12023 – 31[x2] + 2 LE!] Il ] = –6 [36] .- L[t] → SL[] - 2,(0) = 3 L12) – 3 L[202] + . SLSing s-3-18 = s_ 6s +2 -18 . = s (s-6+2 (sl) | - (sk) (+3) ⑤) Lax] = 3 - s²(sk) (st3) - (S-6) (-3) (-)(3) TT + s 5+5 + (-) (5ا ن کے تمام قوا + + = = (ع) به ( . in o Sebstitute Now, 30 + لا SLCx ] = = - 1 - ، Ilaj د - - - - دو - .. - 6S330s - عاما فیدBy partial fraction 13 167 IT 10 LIE = + 무 - ] - KoN) = 13 FL] LJ + C) sale) = p - et + ② Hence 쪽 it) = + + 1 | 55(t) - - per

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