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Ordinary Differential Equations

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

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)

Matlab Program to Model a Situation

Suppose that a rabbit is initially at point (0,100) and a fox is at (0,0). Suppose that the rabbit runs to the right at speed Vr = 5 ft/sec and the fox always runs toward the rabbit at speed Vf = 6 ft/sec. Write a Matlab program that determines to within 1 second, when the fox catches the rabbit. The program should also plot rab

Sketch direction fields for the following ODE's

Sketch the direction fields for the following ODE's. Make use of isoclines wherever possible. a. y' = y - x + 1 b. y' = 2x c. y' = y - 1 d. y' = xsquared + ysquared - 1 e. y' = y - xsquared Please note y'=y prime. It looks diff, when i see the ? #2. In each direction field above sketch integral curves for which

Using Euler's method

Y'= 1/2 - (X)+2x when y(0)=1 Find the exact solution of ___ O/ <<note!!!! I don't know how to put in a zero with a line going across to make a pheee. 1a. Let h=.1 use euler & improved to approximate to get "Phee" of .1, phee of.2, and phee of .3