Explore BrainMass

# Ordinary Differential Equations

### 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

### Systems of ODEs: Elimination

Find a general solution to the system: x1' = -3x1 + x2 x2' = -4x1 + 2x2.

### 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 ?

### Initial Value Problem - Unique Solution?

Determine whether the given initial value problem has a unique solution (using Theorem 1). *Please see attachment for problem (Direct "yes/no" answer is fine)

### General Solution : ODE's

Find the general solution of the ODE below: y" + 2y' + 101y = 0

### First Order Ordinary Differential Equations

Problem A: Suppose that a giant HD-ready television of mass m falls from rest towards earth and its parachute opens at time t=0. when its speed is v(0)=v0 Since the TV is massive assume the drag force is proportional to the square of the velocity. Write a complete model for the velocity v(t) What is the asymptotic behavi

### How to Solve an Equation using Integration Factor

Solve the linear Differential Equation (see attachment) y'-y=exp(2x) y(0)=0 y"+6y'+10y=0 2yy'=1-y^2 y(0)=-2.

### Mechanical displacement - Steel ball problem

A steel ball weighing 128 pounds (mass= 4 slugs) is suspended from a spring. This stretches the spring 128/485 feet. The ball is started in motion from the equilibrium position with a downward velocity of 9 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet p

### Ordinary Differential Equation : Change of Variables

Solve {see attachment} for y(x) using the change of variables z = y + x.

### Solve a 2nd order ODE.

Use methods of undetermined coefficients to find one solution of: y'' + 2y' +2y = (10t+7)e^(-t)cos(t)+(11t+25)e^(-t)sin(t)

### Solve a homogenous 2nd order ODE : Cauchy-Euler Equation

Find y as a function of x if: (x^2)(y'') + 19xy' +81y = x^2 y(1) = 9 y'(1) = -3 Hint: First assume that at least one solution to the corresponding homogeneous equation is of the form . You may have to use some other method to find the second solution to make a fundamental set of solutions. Then use one of the two metho

### 2nd Order Ordinary Differential Equations

Find particular solution to differential equation 3y'' + 4y' + 1y = 1t^2 -2t + 2e^(-3t)

### Evaluate: A Second Order ODE

Use the method of undetermined coefficients to find one solution of : y'' - 16y' +101y = 16exp(8t)cos(6t)+16exp(8t)sin(6t)+1*1

### Solution to Second Order ODE

Find solution of: y'' - 2y' + y = 16exp((5)t) y(0)=1 y'(0)=6

### Question about Second Order ODE

Find y as a function of x if (x^2)(y'')-7xy'-9y = x^2 y(1)=6 y'(1)=8

### Ordinary first order differential equation

Find all solutions to the ODE yy'= (1-y^2) sin x. (When dividing by 1-y^2, be careful that you don't lose any solutions). NOTE: y2 = y squared Please see attached file for full problem description.

### Second order ODE

Find y as a function of t if 64y'' + 32y' +4y = 0 y(5)=6 y'(5) = 5

### Second order ODE

Find y as a function of t if 16y'' - 88y' +121y = 0 y(0) = 4 y'(0) = 9

### Second order ODE

Find y as a function of x if: (x^2)(y'') - 5xy' -16y = 0 y(1)=2 y'(1)= 9

### Find the center of mass of the region

Please see the attached file for full problem description. --- Here is the problem: Find the center of mass of the region bounded by the parabola y = 8 -2x^2 and the x-axis a) if the density lambda is constant and b) if the density lambda = 3y

### First order ordinary differential equation

In order to solve differential equations, it is helpful to classify them as belonging to one or more categories. In this entry we will consider three common classes of first order ordinary differential equations (ODEs): separable, exact and linear. We will show how each class is defined.

### Initial Value Functions

This question is part of a study guide for my final test. Solve the following initial value problem. (see attached for problem) Thank you

### Ordinary differential equations

(d^2 * y)/(d * t^2) + 6 * (dy/dt) + 9y = 0 y(0) = 10, y'(0) = 0

### Alternative to Euler's Method Approximation

Solve a Function (see attached) Explain why the Euler's method cannot be used to approximate y(2)

### Sturm-Liouville Problem: Prufer Equation

Consider the Sturm-Liouville problem (pu') + Vu = 0 for the function u(x), with p(x) > 0 and V(x) = q(x) + lambda p(x). (a) Perform the Prufer substitution u - r sin theta and u'p = r cos theta and obtain the Prufer equations for the amplitude r(x) and the phase theta (x): r' - 1/2 ((1/p) - v) r sin 2 theta, theta' = (1/p)

### Separable/Homogeneous Equation

State if the equation is separable or homogeneous: (x^2 + y^2) (dy/dx) = 5xy

### How to Solve an Initial Value

Solve the initial value problem; it is not necessary to find all solutions of the equation: xy'=y(y-2), y(3)=2.

### Solving First Order Separable Ordinary Differential Equation With Initial Value

Solve the initial value problem dy/dx=(3x^2+4x+2)/[2(y-1)], y(0)=-1

### Initial Value Problem, Ordinary Differential Equation: Jordan and Diagonalization

Find the solution of the system X' using the "diagonalization" technique (actually the Jordan form in this case) Please see the attached file.

### Ordinary Differential Equations Integration

I would like someone to introduce me to ODE and answer questions as they arise.