# 2nd order differential equation

1. Aug 4, 2011

### NEGATIVE_40

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

n/a

3. 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: Aug 4, 2011
2. Aug 4, 2011

### SteamKing

Staff Emeritus
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?

3. Aug 4, 2011

### vela

Staff Emeritus
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.

4. Aug 4, 2011

### NEGATIVE_40

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

thanks.

5. Aug 4, 2011

### icystrike

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

6. Aug 4, 2011

### 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.

7. Aug 4, 2011

### HallsofIvy

Staff Emeritus
If you had tried Ax, then (Ax)''= 0 so the equation would have been 16Ax= 3.36. The left side has an "x" and the right side doesn't. May I ask why you are doing this problem? I would imagine it is because you are taking a course in differential equations but I cannot imagine you having a homework problem like this if you are not in a chapter of your textbook that has a detailed description of "Undetermined Coefficients" as this method is called.