looking for value of existense differential equation

Consider the differential equation x ′ = x cos(at) . For what values of (t, x) can solutions not be guaranteed? how do i find those values of (t,x)

i have :

syms x(t)
ode = diff(x,t) == x/(cos(a*t));
 xsol = vpa(dsolve(ode))

Answer 1

[madhan ravi]

Where there is an aymptote(discontinuity) , the solutions cannot be guaranteed