Trigonometric Functions of Differential Equations : Eliminate the arbitrary constants from the equation: y = c cosh(x/c) , ( the catenary ).

Eliminate the arbitrary constants from the equation: y = c cosh(x/c) , (the catenary).

Find the differential equations of all circles of radius a.

Find the differential equations of all circles of radius a.

Find the differential equations of all circles that pass through the origin.

Find the differential equations of all circles that pass through the origin.

Find the differential equations of all circles of radius a (whatever their radii or positions in the plane xOy).

Find the differential equations of all circles of radius (whatever their radii or positions in the plane xOy).

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.]

Show that the zeros of two linearly dependent, nontrivial solutions of the following equation coincide. y" + A(t) y = 0

Show that the zeros of two linearly dependent, nontrivial solutions of the following equation coincide. y" + A(t) y = 0

Solve the ODE : (y'[x])^2 + x*y'[x] = y[x] + x

Solve the ODE :(y'[x])^2 + x*y'[x] = y[x] + x

Eigenvectors, Eigenvalues, Critical Points and Trajectories in the Phase Plane

(i) Find eigenvalues and eigenvectors: (ii) Classify the critical point (0,0) as to type and determine whether it is stable or unstable: (iii) Sketch several trajectories in the phase plane. --> =(-7 10) --> x' (-5 8) x

Systems of Differential Equations

Show your argument in details you can use Maple to assist you in long calculations. YOU CANNOT USE dsolve command! Consider the following system 1) Find the general solution the systems 2) Find the solution that satisfies and . Is the solution unique? 3) Plot a (the) solution of question 2). (See attached ...continues

Eigenvalues, Eigenvectors and Trajectories in the Phase Plane

(i) Find eigenvalues and eigenvectors. (ii) Classify the critical point (0, 0) as to type and determine whether it is stable or unstable. (iii) Sketch several trajectories in the phase plane. Please see the attached file for the fully formatted problems.