Answer:
a) 0 is stable when n = odd
b) 0 is semi-stable when n = even
c) 0 is unstable when n is odd
Step-by-step explanation:
Th differential equation for this question
dx/dt = x^n
n = positive integer
<u>a) value of n where 0 is stable </u>
0 is stable when x^n is replaced with -x^n
because considering n to be an odd number
-x^n > 0 when x < 0 while -x^n < 0 when x > 0
∴ In this scenerio we can conclude that 0 is stable when n = odd number
<u>b) Value of n where 0 is Semi-stable </u>
assuming n is an even number
x^n > 0 for all the values of x
<u>c) Value of n where 0 is unstable </u>
lets assume n is odd
when n < 0, xⁿ < 0
when n > 0, xⁿ > 0
i.e. 0 is asymptotically unstable when n is an odd number
