Thus we can write
x c x(n x)t 1 , where c1 is the Positive constant
Now we can write
c xn x
dt
dx
1
On solving, we have
nc t A
n x
x
1
log
Where A is integration constant which can be calculated after taking initial conditions
Initial conditions
If at
0 & 0
t 0;n n x x then we can write
0 0
0
log
n x
x
A
Now putting this value in the above equation we have
0 0
0
1
log log
n x
x
nc t
n x
x
But if
x0
1
, After simplification we have
nmt nc t
x n e ne 1
[ 1 ]
0
or
nc t
nc t
n e