Find the solution to dydt 8y satisfying y3 2SolutionSepara

Find the solution to dy/dt = 8y satisfying y(3) = 2

Solution

Separating the variables, we have

                                      dy/y= 8dt........................(1)

Integrating this , we obtain

                                     ln y = 8t +ln C., say....................(2)

So                                   y =C e^8t ...................................(3)

At t =3, y=2. Substituting in (2) ,

                                        2= C e²⁴

         or                            C =2e^-24

So the required solution is y(t) =2e^-24 e^8t