1. Does the formula z represent an ordinary differential equation or a partial differential equation? Find its order, the dependent and independent variables and determine whether it is linear or non-linear. dy I 2. Use Implicit Function Theorem to verify whether the relation ry cos(x - y) = C defines an implicit solution of the differential equation | z t y ry tan(r - y) 2 + y tan(x - y) where C is a constant. Show your calculations and briefly explain your answer. 3. Find a general solution of the differential equation 4 (4 sec y 1). record -4t cos(y) Start by identifying the type of the equation and the method used. Leave your answer in an implicit form if necessary. 4. Solve the following initial value problem for y(r): Simplify your answer as much as possible. T cos(y)y' + sin(y) = 0, y(0) = -