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Ordinary Differential Equations

Differential equation solved with variables separable method

Let x: [0, infinity) -> R and y: [0, infinity) -> R be solutions to the system of differential equations: x' = - x y' = - sin y With initial condition: x(0) = y(0) = alpha, where alpha belongs to [0, pi) (a) Show that |x(t)| =< alpha for all t >= 0 (b) Show that | y(t) -

Series Solutions of Second Order Linear Equations

Verify that x0=0 is an ordinary point of the differential equation: y''+ xy' + 2y = 0 Find two linearly independent solutions to the differential equation in the form of a power series about x0=0. If possible, find the general term in each solution. Write the general solution Verify that x0=0 is an ordinary point for the

Solving an Ordinary Differential Equation

DP/dt = m(a0)[exp(-z1)t] - (z2/z1)P Solve this differential equation with a = ao at t=0 and a=a at t=t to show that: P = [mz1(a)] / [z2 - z12] + [mz1(ao) / (z12- z2)](a/ao)^(z2/z12) Where the last term in this equation is a/ao "raised to the power of" z2/z12 ---

Solving a Particular solution to an Ordinary Differential equation

See attached problem. PLEASE NOTE!!! I have noted in the problem statement that I have solved the homogeneous portion of the differential equation, and I need assistance in solving for the particular solution and finally the whole solution. I have gotten 2 responses from other OTA's that are as follows: "The point is that y

Euler's and Rutta methods

Discuss how to choose the step size h.... missing.jpg contains the given differential equation to the question in the other *jpg file.

Explicit Euler Method

Was Euler the ancient fortune-teller? He almost was. One of his principles, the explicit method says that your future days could be predicted from your present day knowing your past provided your time frame is not too large. Have a look at the solution to a system of non-linear differential equations system using explicit or

Ordinary Differential Equations: Boundary Value

Solve each of the following ODE's for y(x): (a) y" + 16y = 0 with y(0) = 1 and y'(0) = 0. (b) y" + 6y' + 9y = 0 with y(0) = 1 and y'(0) = 0. (c) y"' - y" + y' - y = 0 with y(0) = 1 and y'(0) = y" (0) = 0.

Ordinary Differential Equation

Ordinary Differential Equation Determine if the following system has nay non-constant solutions that are bounded, i.e. do not run off to infinity in magnitude x' = x(y - 1) y' = y(

Show that this system is a Hamiltonian system.

Please give me a step-by-step solution to this attached ODE. Consider the following system: x' = -2y y' = x/2 a. Show that this system is a Hamiltonian system. b. Us a Hamiltonian to sketch the phase portrait for this system.

Space Factor, Time Factor, Eigenvalues and Sturm-Liouville

7. Consider the differential equation ut =1/2 uxx + ux for 0 <x < pi, t > 0 with boundary conditions u(0,t) = u(pi,t) = 0. (a) Separate variables and write the ordinary differential equations that the space factor X(x) and the time factor T(t) must satisfy. (b) Show that 0 is not an eigenvalue of the Sturm-Liouville proble

ODE: Variation of Parameters

Please see the attached file for the fully formatted problems. One solution of the equation attached is y(t) = t. Find the general solution. Use variation of parameters to find a particular solution of the equation attached.

Phase Plane

Solve y" + w^2y = 0 w= the symbol omega subscript zero (0).

Unique Equilibrium Levels : Lead Levels in Blood

For any positive values of the input I and the rate constants k, show that system (3) has a unique equilibtium solution x1=a, x2=b, x3=c where a,b and c are all positive. Building the Model ODEs Apply the Balance Law to the lead flow through the blood, tissue, and bone compartments diagrammed in Figure 61 .2 to obtain a syst

Determine Inertia, Damping, and Stiffness

See attached file. P228#2 Using the paradigm, What are the inertia, damping, and stiffness for the equation ? If y>0, what is the sign of the 'stiffness constant'? Does your answer help explain the runaway behavior of the solutions ?