Existence and Uniqueness (Picard’s Theorem)In each case the theoremdoes not apply(dydx=11-xy(1) =1has no solutionsf(x,y) =11-xis not defined (let alone continuous) at(x,y) = (1, 1)-2-112y-2-112xDot doesn’t know whether to travel up or down!
(dydx=12yy(0) =0has two solutionsy(x) =±√xf(x,y) =12yis not defined at(x,y) = (0, 0)-2-112y-2-112xDot could move up or down from origin