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Ordinary Differential Equations

2nd order ODE

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

Solving an ODE

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.

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

Classification of first order ordinary differential equations

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

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

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

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