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.

Homework Equations

n/a

The Attempt at a Solution

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

 

[SteamKing]

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?

 

[vela]

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

[tex]y_p = A $$so doing that I get A = 0.21, which gives me the correct solution.<br /> <br /> thanks.$$[/tex]

 

[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.

 

[HallsofIvy]

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

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.