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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