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we-have-a-system-made-up-of-two-cells-x-and-y-Both-of-the-cell-types-are-dividing-and-dying-X-type-cells-also-differentiate-into-Y-type-cells-The-dynamics-of-this-system-interms-of-size-of-X-and-Y




Question Number 207154 by Wuji last updated on 07/May/24
we have a system made up of two cells  x and y. Both of the cell types are  dividing and dying. X type cells also  differentiate into Y type cells. The  dynamics of this system interms of  size  of X and Y population is given below.  calculate the steady state of this system  (dx/dt)=−3x   (dy/dt)=2x−2y
wehaveasystemmadeupoftwocellsxandy.Bothofthecelltypesaredividinganddying.XtypecellsalsodifferentiateintoYtypecells.ThedynamicsofthissystemintermsofsizeofXandYpopulationisgivenbelow.calculatethesteadystateofthissystemdxdt=3xdydt=2x2y
Answered by mr W last updated on 07/May/24
(dx/x)=−3dt  ⇒x=C_1 e^(−3t)   (dy/dt)+2y=2C_1 e^(−3t)   ⇒y=((2C_1 ∫e^(2t) e^(−3t) dt+C_2 )/e^(2t) )=−2C_1 e^(−3t) +C_2 e^(−2t)
dxx=3dtx=C1e3tdydt+2y=2C1e3ty=2C1e2te3tdt+C2e2t=2C1e3t+C2e2t

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