Let's solve the initial value problem given by the differential equation dy together with the initial condition: if x = 0 then y = 1 . We begin by writing our differential equation in the form f(y) dy = g(x) dx where . f (y) = . g(x) = Integrating both sides of this equation gives fly) dy = g(z) dx . After integrating, we can merge the two constants of integration into a single constant C to the get form Iny = 2x6 + C. Using the initial condition, we get C = Hence the solution to the original initial value problem is y =