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 t ...continues

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.

proportional rate

A bacteria culture starts with 760 bacteria and grows at a rate proportional to its size. After 2 hours there will be 1520 bacteria. Express the population after t hours as a function of t.

mixing problem

a tank contains 1320 L of pure water. A solution that contains .01kg of sugar per liter enters a tank at the rate 3L/min. The solution is mixed and drains from the tank at the same rate. Find the amount of sugar after t minutes as a function of t.

help solving separable equation in mixing problem

A tank contains 1320L of pure water.A solution that contains .o1kg of sugar per liter enters a tank at the rate 3L/min The solution is mixed and drains from the tank at the same rate. Solve for function of t So far I have the equation: dy/dt = (.01)(3)-(y(t)/1320)*(3) but I guess I am not understanding how to solve this ...continues

exact equation

The following differential equation is exact. Find a function F(x,y) whose level curves are solutions to the differential equation: ydy-xdx=0 "F(x,y) such that the solutions are F(x,y)=c for an arbitrary constant c".

explicit/implicit solutions to diff. equation

Find an explicit or implicit solutions to the differential equation: (x^2 + 4xy)dx + xdy = 0 "F(x,y) such that the solutions are F(x,y)=c for an arbitrary constant c".