Unformatted text preview: 1 Solutions The integrating factor is
Integrating and simplifying gives
condition
implies . Thus .
. The initial so input rate for Tank 2: input rate
g
min
output rate for Tank 2: 29 output rate The initial value problem for Tank 2 is thus L
min g
L L
min g
L g
.
min When this equation is put in standard form we get The integrating factor is . Thus Integrating and simplifying gives The initial condition implies so Section 1.5
1. In standard form we get
which is homogeneous since
the degrees of the numerator and denominator are each two. Let
.
Then
and so
. Separating variables gives
. Integrating gives
Substituting gives . So
. . ...
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 Fall '08
 BELL,D
 Boundary value problem, input rate, output rate

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