PROBLEMS 1. Consider the rst order DDE. Solve the Initial Value Problem. w' = e'th: w() = 2 where w is the dependent variable which is a function of the independent variable 1:. Be sure to calculate the interval of existence for the solution and provide the interval with your solution. 2. Find the general solution for this ODE, di D.1+ 200i = 5 dt wherei is the dependent variable which is a function of the independent variable t. 3. A tank in the form of a rightcircular cylinder standing on end is leaking water through a hole in its bottom. When friction is ignored, the rate of change of the height of the water in the tank is given by this equation: so) = r2 cosh where h. is the height of the water in feet, I: is the time in seconds. and r is the ratio of the hole diameter to the tank diameter. Part A: Solve the Initial 1F.i'alue Problem when r = 0.1 and MEI] = 6. Part B: Given the I'U'P in Part A, how long will it take the tank to drain completely