Question
(a) Let S be the set of solutions y(t) to the differential equation dy/dt = -y for t> 0. With addition and scalar multiplication of elements defined in the usual way, is S a vector space?
(b)Let T be the set of solution y(t) to the differential equation dy/dt = 1 - y for t > 0. With addition and scalar multiplication of elements defined in the usual way, is T a vector space?
(b)Let T be the set of solution y(t) to the differential equation dy/dt = 1 - y for t > 0. With addition and scalar multiplication of elements defined in the usual way, is T a vector space?