Math 2280-2 Example 5.6.2 (three tanks cascade with salty water coming in) with(LinearAlgebra): A := Matrix(3,3,[-1/2,0,0, 1/2, -1/4, 0, 0, 1/4, -1/5]);

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xp := t -> Vector([40,80,100]);

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Phi := t -> MatrixExponential(A*t);

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Phi(t);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKFNASSM=

c:= -MatrixInverse(Phi(0)) . xp(0);

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x := t-> Phi(t) . c + xp(t);

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x(t);

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plot(x(t),t=0..60,color=black);

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

TTdSMApJM1JUQUJMRV9TQVZFLzkxNjc5MlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyoiJCIkIyEiIiIiIyMiIiJGKSIiIUYsI0YoIiIlI0YrRi5GLEYsI0YoIiImNiI=TTdSMApJNFJUQUJMRV9TQVZFLzIzMDIxNDBYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMqIiQiJC0lJGV4cEc2IywkJSJ0RyMhIiIiIiMsJi1GKDYjLCRGKyNGLSIiJUYuRichIiMsKC1GKDYjLCRGKyNGLSIiJiMiI0QiIiRGMCEjNUYnI0Y7Rj4iIiFGMCwmRjAhIiZGN0Y7RkFGQUY3NiI=TTdSMApJNFJUQUJMRV9TQVZFLzEwMDI1MTJYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIkIiQhI1MhIyEpISQrIjYiTTdSMApJNFJUQUJMRV9TQVZFLzEwMjI1NzZYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIkIiQsJi0lJGV4cEc2IywkJSJ0RyMhIiIiIiMhI1MiI1MiIiIsKC1GKTYjLCRGLCNGLiIiJSEkZyJGKCIjISlGOkYyLCotRik2IywkRiwjRi4iIiYjISUrRCIiJEY0IiQrKUYoIyEkKyNGQyIkKyJGMjYi