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)

Answer:

The particular solution of the differential equation is:

y = 80exp (t / 2)