I must complete the following exercise by the end of tonight:

It is suggested that we use the following formulation of the Gronwall inequality:Let such that

, ,

where are continuous on . Show that the solutions of the IVP

,

exist on .

Also, I suspect (though I am not certain) that the following theorem, part of the unit of this exercise, might be useful:Suppose that is a continuous solution of

, ,

where are continuous and for . Then

, .

Any help would be much appreciated!Let , , , , and is bounded. Then every solution of , , exists on .