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