I am going to quote an article below and there is a part I would like clarification.I do not understand why chaotic differential systems do not have an analytical solutions. In the simplest form,an equation such as this one [sin(x) + x - 0.5 = 0] does not have an analytical solution i.e it can be only solved numerically. 1.What would be its equivalent for a differential system not having a analytical solution? 2.When the differential equation/system gives a different response for different initial conditions,how does it imply "not having a analytical solution"? I'm a novice.