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Differential EquationsSuperchallengeSystems of Differential Equations

Systems of Differential Equations · Superchallenge problem

Consider x1′=−x1+x2, x2′=−x2+x3, x3′=−x3x_1'=-x_1+x_2,\ x_2'=-x_2+x_3,\ x_3'=-x_3 with x(0)=(0,0,1)\mathbf x(0)=(0,0,1). Find the maximum value of x1(t)x_1(t) over t≥0t\ge0.