Question

Use variation of parameters to solve the given nonhomogeneous system. dx = 5x - 5y + 5 dy dt = 4x - 4y - 1 (x(t), y(t)) Submit Answer Submit Assignment

Answer 1

Differentiat is writ. 't, we get 4 dx dt dt d! y (5x -54 +5)-4. dy 4. de [using is d22 d d2 ay ay +20x-204 +20 - zoy + 20 -4 dny 1 + 5.94 you -204 +20+5. +5. ( ay tuy + [using is dy dy? y day - 299 +20 t 5 day + 2gy + dt? + 5 dy dt dt? + 25 d y dt? 03 dy dt 25 which is the same differential equ as civ So, similarly, can find the general solution. general solution 4 The of equ ix i -254-25 Thus, Eqr cvii) & (X) beth are solutions of system O. Ay

Thus, y 1 et te are two linearly independent solution. So YR 1. da + ₂ es w w et 25 dat dt -y, J exf 25.11 et | 25ete + e + 25 fet) -254-257 :) J 25 dt + - 25 P. 1 cris How, General solution of un X + PI nct) Gt Get - 25t - 25 cvity Notes comparing eqh Livy with det functions of + P du at thx = R where either are the + or constant. Q=0 R=25

solutions נייייי P9H WP * Susy + 5 40-44 3-0 de Differentiate i + d'x dr = 5 de uw IP Using 5 d dt it in ciri, waget, 25 (4X_uy 1) 20x + 20yrs -204 +5 +4.59 Р P = 50 7P P. at 5 dy -200 +5+41 MyP SP ar it du at - 200 + 5 + 200 +20 MP dM at + 20 H? dy at = 25 ling HP can be written an al 2 (0²-D)X = 25 Now, fint all we have to find complementary function (C. F) of eq" ling Them Auxiliary E is 20 m-o, Then, +628? - CUB How, we have to find particular integrals P1.) from CN) wronskian (W) of I & I = Greet How, find

1 Pg 4) - 252-25 X(t) = C. + Get Vii Y = d, tdzet -25 t - 25 where, d, = ctc, dy= usa Both eq auild & N. are the required salt of system 4 En can be written as Y ) = (C+6) + - 258-25 9 ) G + - 257 - 19 i) 4 met & Greet - 25 t - 25 Henia equ (xi) & (xiij both are also required solution,