Consider the following initial value problem: y' + ty³ =tan(t), y(-5) = -1 a. Rewrite the differential equation, if necessary, to obtain the form y' = f(t, y). f(t, y) = b. Compute the partial derivative of f with respect to y. Determine where in the ty-plane both f(t, y) and its derivative are continuous. Be sure to write these functions on your paper, including the process that shows how you arrived at the given expressions. c. Find the largest open rectangle in the ty-plane on which the solution of the initial value problem above is certain to exist for the initial condition. t interval is: ( y interval is: ( )

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