# Second order differential equation

## Homework Statement

if given the general solution to a differential equation
y(t)=a cos t + b sin t + ((cos wt)/1-w^2),
Find out how long it takes the solution to approach the steady state solution.
original second order differential equation:
y'' + y = cos wt such that 0 < w < 10

## The Attempt at a Solution

I am not sure where to begin.

## Answers and Replies

rock.freak667
Homework Helper
So for y'' + y = cos wt

What is your homogeneous solution?

EDIT: Remember that your general solution will be y=yh+yss.

Last edited:
Mark44
Mentor

## Homework Statement

if given the general solution to a differential equation
y(t)=a cos t + b sin t + ((cos wt)/1-w^2),
The good news is that you are being very diligent in your use of parentheses, but the bad news is that some of them aren't in the right place. You should write the last expression above as cos(wt)/(1 - w^2). As you have it, this expression would be read as cos(wt)/1 - (w^2), or cos(wt) - w^2, and I'm pretty sure that's not what you intended.
Find out how long it takes the solution to approach the steady state solution.
original second order differential equation:
y'' + y = cos wt such that 0 < w < 10

## The Attempt at a Solution

I am not sure where to begin.
A good start would be to find out what the term "steady state solution" means.