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)
Answer:
The particular solution of the differential equation is:
y = 80exp (t / 2)