Understanding solution to differential equation in Mathematica

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?

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

  • 1.just means1.0. In programming languages this is different from a simple1which usually means an integer while1.0means a real number. InMathematicaa 1 is a perfectonewith infinite precision, while1.0has only machine precision.

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

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