Understanding solution to differential equation in Mathematica

Question

I got a solution using DSolve as :

Function[{t}, -((
   1. (2. + k (-1. - 2. t) + k^2 (-0.5 + 1. t + 1. t^2)))/k^3) + 
  E^(-1. k t) C[1]]

What does '.' mean and '()'? For example, in the case of '2.+k(-1.-2.t)', what does it mean? How to translate it to normal Math notation?

Answer 1

Pretty simple because the first one is regularly used in languages like C and Java too and the second one actually is math-notation. Therefore,

• 1. just means 1.0. In programming languages this is different from a simple 1 which usually means an integer while 1.0 means a real number. In Mathematica a 1 is a perfect one with infinite precision, while 1.0 has only machine precision.

• k(1-t) just means k*(1-t). Parenthesis are used like in normal math too.