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| PAGE: 639 | SET: Exercises | PROBLEM: 16 |
The differential equation is 
.
(a)
Find the solution of the differential equation.
Apply integral on each side.
Apply power rule of integral : 
.
.
.
At the initial time 
and 
.
.
Susbtitute 
in 
.
Therefore, the solution of the equation is 
.
(b) Find the value of 
when 
.
As 
tends to left side of then the condition is 
.
When there is a small positive number to a negative exponent, then the value is very positive number.
Hence, 
the expression approaches to 
.
Therefore, 
.
(c)
The equation is .
The doomd day will happen at 
.
The number of rabits breed initially is 
.
The numbers of rabits breed after three months are 
.
The prolific breed of rabbits has the growth term is 
.
The function is , where the growth term is 
.
Compare equations 
and .
The value of 
.Susbtitute 
, 
,
and 
in .
Substitute 
, , in .
The doomsday will happen after 
.
(a) The solution of the equation is .
(b) at .
(c) The droomday will happen after 
.
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