Question Number 41726 by Necxx last updated on 11/Aug/18
$${Tank}\:{T}_{\mathrm{1}} \:{and}\:{T}_{\mathrm{2}} \:{initially}\:{contains} \\ $$$$\mathrm{100}{gal}\:{of}\:{water}\:{each}.{In}\:{T}_{\mathrm{1}} \:{the} \\ $$$${water}\:{is}\:{pure},{whereas}\:\mathrm{150}{lb}\:{of} \\ $$$${fertilizer}\:{are}\:{dissolved}\:{in}\:{T}_{\mathrm{2}} .{By} \\ $$$${circulating}\:{liquid}\:{at}\:{a}\:{rate}\:{of} \\ $$$$\mathrm{1}{gal}/{min}\:{and}\:{stirring}\:{the}\:{amount} \\ $$$${of}\:{fertilizer}\:{y}_{\mathrm{1}} \left({t}\right)\:{in}\:{T}_{\mathrm{1}} \:{and}\:{y}_{\mathrm{2}} \left({t}\right) \\ $$$${in}\:{T}_{\mathrm{2}} \:{change}\:{with}\:{time}\:{t}. \\ $$$$\left.{a}\right){with}\:{a}\:{schematic}\:{diagram}\:{write} \\ $$$${the}\:{model}\:{linear}\:{equations}\:{for} \\ $$$${the}\:{mixing}\:{problem}. \\ $$$$\left({b}\right){determine}\:{the}\:{eigenvalues}\:{and}\circledast \\ $$$${and}\:{eigenvectors}\:{of}\:{the}\:{derived} \\ $$$${equation}. \\ $$