It is problem of finding the differential equation of all circles of radius a.

Differential Equation (XIII) Formation of Differential Equations by Elimination It is problem of finding the differential equation of all circles of radius a.

It is the problem of finding the differential equation of all circles that pass through the origin.

Differential Equation (XIV) Formation of Differential Equations by Elimination It is the problem of finding the differential equation of all circles that pass through the origin.

It is the problem of finding the differential equation of all circles of radius (whatever their radii or positions in the plane xOy).

Differential Equation (XV) Formation of Differential Equations by Elimination It is the problem of finding the differential equation of all circles of radius (whatever their radii or positions in the plane xOy).

Differential Equations

(See attached file for full problem description with equations) --- Differential Equations: You are allowed to use any algebra software to assist you. However, explain in details what you are doing. Consider the following mechanical vibration motion with forcing where b, k are positive constants. We will assume the underdamped condition Problem 1: Show that the corresponding homogeneous equation has two linear independent solutions What are in terms of b, k? Problem 2: Let f(t) be a continuous function on [0, ). Use the variation of constants method to show that the general solution to (0.1) is given by the formula ---------------- (0.2) Problem 3: Ass... click for more

Sup norm question

Let X be a compact metric space and Y be a normed space. Prove that if f_n belongs to C(X,Y), then lim_n f_n = f_o in the Sup norm if and only if lim_n f_n = f_o uniformly in X. [ Note: Sup norm: ||f|| = Sup||f(x)|| for every x in X.]