Forced harmonic oscillator

Consider the forced harmonic oscillator: y'' + by' + ky = g(t) + y0 where the forcing is made up of two parts, constant forcing (y0) and forcing (g(t)) that changes over time. a) Let w(t) = y(t) - y0/k. Rewrite the forced harmonic oscillator equation in terms of the new variable w. b) In what ways are the solutions of the two equations the same?

Solve the differential equation by using convolution

Using convolution, solve this differential equation y"+4y'+13y=(1/3)e^(-2t)sin3t

Power series

(x+1)y"-(2-x)y'+y=0 y(0)=2,y'(0)=-1 use power series methods to solve differential equation with given initial values

Define Picard’s method for solving differential equations.

Solve the differential equation dy/dx = f(x,y) with initial condition y(xo) = yo by using Picard’s Method. Find the successive approximation of the solution by using Picard’s method (upto 3rd approximation) dy/dx = x + y, y(0) = - 1

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.