The particular solution of the differential equation dy dt equals y over 2 for which y(0) = 80 is

First we write the differential equation:
 dy / dt = y / 2
 We solve the equation by means of the separable variables method.
 We have then:
 2 (dy / y) = dt
 We integrate both sides of the equation:
 2Ln (y) = t + C
 We clear y:
 Ln (y) = t / 2 + C / 2
 The constate remains unknown, therefore, rewriting:
 Ln (y) = t / 2 + C
 y = exp (t / 2 + C)
 y = exp (t / 2) * exp (C)
 y = C * exp (t / 2)
 We use the initial condition to find the value of the constant:
 80 = C * exp (0/2)
 C = 80
 Finally:
 y = 80exp (t / 2)
  
 The particular solution of the differential equation is:
 y = 80exp (t / 2)