Tank T_1 and T_2 initially contains 100gal of water each.In T_1 the water is pure,whereas 150lb of fertilizer are dissolved in T_2 .By circulating liquid at a rate of 1gal/min and stirring the amount of fertilizer y_1 (t) in T_1 and y_2 (t) in T_2 change with time t. a)with a schematic diagram write the model linear equations for the mixing problem. (b)determine the eigenvalues and⊛ and eigenvectors of the derived equation.


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Question Number 41726 by Necxx last updated on 11/Aug/18

$T a n k T_{1} a n d T_{2} i n i t i a l l y c o n t a i n s$ $100 g a l o f w a t e r e a c h . I n T_{1} t h e$ $w a t e r i s p u r e, w h e r e a s 150 l b o f$ $f e r t i l i z e r a r e d i s s o l v e d i n T_{2} . B y$ $c i r c u l a t i n g l i q u i d a t a r a t e o f$ $1 g a l / m i n a n d s t i r r i n g t h e a m o u n t$ $o f f e r t i l i z e r y_{1} (t) i n T_{1} a n d y_{2} (t)$ $i n T_{2} c h a n g e w i t h t i m e t .$ $a) w i t h a s c h e m a t i c d i a g r a m w r i t e$ $t h e m o d e l l i n e a r e q u a t i o n s f o r$ $t h e m i x i n g p r o b l e m .$ $(b) d e t e r m i n e t h e e i g e n v a l u e s a n d ⊛$ $a n d e i g e n v e c t o r s o f t h e d e r i v e d$ $e q u a t i o n .$
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