Let A 0 be a real number and p 0 Consider the function r 0

Let A > 0 be a real number and p = 0. Consider the function .r: [0, infinity) rightarrow R defined by x(t) = A(t + 1)1/p. The function x(t) is a solution to the FODE x\'(t) = x^1 - P(t) for some choice of ohm a global solution to the FODE x\'(t) = x^1 - p(t) for some choice of ohm a solution to the FODE x\'(t) = A^p/p x^1 - p(t) for some choice of ohm a global solution to the FODE x\'(t) = A^p/p x^1 - p(t) for some choice of ohm None of the above

Solution

x(t) = A(t+1)^1/p

x \'(t) = A/p (t+1)^1/p-1

x \'(t) = A(t+1)^1/p * (1/p)(t+1)^-1

x \'(t) = x(t) * (A^p/p) [A(t+1)^1/p]^-p

x \'(t) = (A^p/p) x^1-p (t)

option (d)