Answer to Question #59455 in Differential Equations for Rita

Question

10 One of the following is not a sufficient conditions for the existence of solution of the first order equation dy/dx = f(x,y), with y(x0)=y0
in a region T defined by |x−x0|<a and |y−y0


i. f is continuous in T

II. f is bounded in T

III. ∂f/∂y is continuous in T

IV. ∂f/∂y is not continuous in T

Answer 1

iV. ∂f/∂y is not continuous in T.