kreyszig 공업수학 solution(솔루션)9판 4장
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작성일 20-11-12 19:10
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Hence a general solution of the system of ODEs is
y 25 [ ] 25 [ ]e0.024t.
y Ay, where A [ ] .
kreyszig 공업수학 솔루션9판 4장,ch4
the new tank, because the limits are 25 lb and 125 lb, as the particular solution shows.
y1 0.004y2 0.02y1
is five times that of the old T2. Ordering the system by interchanging the two terms
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순서
kreyszig 공업수학 솔루션9판 4장 kreyszig 공업수학 솔루션9판 4장 kreyszig 공업수학 솔루션9판 4장
The characteristic polynomial is 2 0.024 ( 0.024). Hence the eigenvalues
are 0 (as before) and 0.024. Eigenvectors can be obtained from the first component
For t 0 this becomes, using the initial conditions y1(0) 0, y2(0) 150,
y(0) [ ][ ]. Solution: c1 25, c2 25.
2. The two balance equations (Inflow minus Outflow) change to
of the vector equation Ax x; that is,
The situation described in the answer to Example 1 can no longer be achieved with
on the right in the first equation and writing the system as a vector equation, we have
this is 0.02x1 0.004x2 0.024x1. This simplifies to
This gives the particular solution
kreyszig 공업수학 solution(솔루션)9판 4장
kreyszig 공업수학 solution(솔루션)9판 4장
For 1 0 this is 0.02x1 0.004x2, say, x1 1, x2 5. For 20.024
where 0.004 appears because we divide through the content of the new tank, which
0.004x1 0.004x2 0. A solution is x1 1, x2 1.
kreyszig 공업수학 solution(솔루션)9판 4장
kreyszig 공업수학 solution(솔루션)9판 4장
레포트 > 공학,기술계열
0.02x1 0.004x2 x1.
y2 0.02y1 0.004y2
설명
y c1[ ] c2[ ]e0.024t.
다.
