# 2nd order differential equation

NEGATIVE_40

## Homework Statement

y''+16y=3.36

This is actually part of a spring question I'm attempting at the moment, and I'm having a mental blank on how to deal with the 3.36.

n/a

## The Attempt at a Solution

I've found the characteristic equation and solution based from that;
$$c_1 cos(4x) + c_2 sin(4x)$$
$$c_1 cos(4x) + c_2 sin(4x) + 0.21$$

Last edited:

Staff Emeritus
Homework Helper
Remember: The general solution to any linear non-homogeneous differential eq. is equal to the soln. to the homogeneous sq. plus the particular soln. to the non-homogeneous eq.
What is your characteristic eq. here?

Staff Emeritus
Homework Helper
You found the homogeneous solution. You need to find the particular solution. Try substituting a trial solution of the form yp=A and solving for A.

NEGATIVE_40
You found the homogeneous solution. You need to find the particular solution. Try substituting a trial solution of the form yp=A and solving for A.

[tex] y_p = A [tex]
so doing that I get A = 0.21, which gives me the correct solution.

thanks.

icystrike
However do you know the rationale for choosing trail function as A instead of A x

NEGATIVE_40
yep. so it isn't a multiple of the homogenous solution. I did a course of DE's a while ago, I just forgot what to do in this case.