Question

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Solve the system of first-order linear differential equations. (Use C1 and C2 as constants.) vi' = -471 42' = - 1v2 (yı(t), yz(t)) =

Answer 1

# Solution : The given that the system of equation ४ - -१५, , ५- -१५, dy -+५ न १dy = ---- →4d= -- = - -40+ c + ०४५~44+ c -42+c ने 1-2 -4-4-C ५- २ -94 Y = Cie where cizé is constant And v. = -12 dy2 = -12 dम → d५2- -dA ५ Sudy2--24- - ०५.)- -*+C ने 42-4+c C 12= et caze is constant - (22

Flence (५९), ५. (A)) = ( Ca", ezt Answer *(2) The given that ५-५-542 ५ - 242 ": 4 ने dY2- gya = 21. 4.dya 2 dt J+dy = 2fd → op५2 = 2+C = पृ2- get to 2 cize is a constant 12 = C, 24 And ५ = ५,-542 dy dt = ५ - १ Ad५]_413 -८३ dt न (D-1) - C24 The Auxiliary equation of equation (2) and but D=m M- 20 m=1 then complementary function (५८ (4) = (2)

73 find the borti culon.31uliom os equalion (1), We 90t. मा) - (10-1) पा(1) ( -2) YHA)= -c, et Hence the general solution is 41 (4) = ५.c(4) +4 (2) ५,12)= Cी (4)= - 129+ C,224 :: (५) (9), ५014)) = (-42+2&, , 24-) Answell