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Calculate-the-generalized-solution-for-the-following-system-of-ODEs-dx-dt-1-2-x-dy-dt-1-2-x-1-4-y-dz-dt-1-4-y-1-6-z-




Question Number 207106 by Wuji last updated on 07/May/24
Calculate the generalized solution for the following  system of ODEs:  (dx/dt)=−(1/2)x, (dy/dt)=(1/2)x−(1/4)y,  (dz/dt)=(1/4)y−(1/6)z
CalculatethegeneralizedsolutionforthefollowingsystemofODEs:dxdt=12x,dydt=12x14y,dzdt=14y16z
Answered by mr W last updated on 07/May/24
 determinant (((−(1/2)−λ),0,0),((1/2),(−(1/4)−λ),0),(0,(1/4),(−(1/6)−λ)))=0  (−(1/2)−λ)(−(1/4)−λ)(−(1/6)−λ)=0  ⇒λ=−(1/2), −(1/4), −(1/6)  V_1 = [((4/3)),((−(8/3))),(1) ]  V_2 = [(0),((−(5/3))),(1) ]  V_3 = [(0),(0),(1) ]   [(x),(y),(z) ]=C_1 e^(−(t/2))  [((4/3)),((−(8/3))),(1) ]+C_2 e^(−(t/4))  [(0),((−(5/3))),(1) ]+C_3 e^(−(t/6))  [(0),(0),(1) ]
|12λ001214λ001416λ|=0(12λ)(14λ)(16λ)=0λ=12,14,16V1=[43831]V2=[0531]V3=[001][xyz]=C1et2[43831]+C2et4[0531]+C3et6[001]
Commented by Wuji last updated on 07/May/24
God bless you, sir
Godblessyou,sir

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