Question

1. Find the general solution by substitution or elimination. (p) -2 + y + 2e+ x - y-et

Answer 1

» Ye = ez+G02 Let 7p = Bet * DYpa ob et Dyp = Bet da Darn-y = rêt - cd -ét ano dy - et Dy axty- It - key = y het ш) DX 0 » Dhe of Dr -DY -2 et Frét vis Duü → 0²4 + DY Du Cj tij rrüi) → D + 2Dx (v) -ét >> D(0+2)x Auxiliary equ i D (0+2)=0 => D=0,-2 y complementary solution X= 4 +Criezt particular integral of (V). be the Let R = A ét - Act Now, Dee ♡ Drap = Aēt -détanêt A=1 * x-e (VI) (t)- ķtup aitezent tek » Ixlt) vii iv) + + Ü) is By + 204 =zet =) DID+2) ya set Auxiliantly ean B (DP2)=0 2 D=0,-2 :v -> abéte zēt -> [B=-2

ci-cē 2 got Yo = -zet siyat) YmYp (vinj >/y (4 egentzett in W,+ lising (wi) & (vi) f (61+₂ e 2t + ēt) - (e3+40 2t zet)=zet (~269 0-24 ét). (ertez-cz) + (-202 + C2 - (4) e 2to o (4-3) This is being + (-22-4) ezt identity into 8 = 0 the system is Hence & C2 94 the final solution of X(t) = at Gezt tet YLE) - (Regd)

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