Method of undetermined coefficients

[s7b]

Hi,

When using the method of undetermined coefficients to solve

2y'' + y' = cos(2x) + 4x + 1

I did it term by term. I figured out the first yp1 for the cos(2x). I'm just not sure what to "guess" as to the form of the yp2 for 4x+1

Does anyone know what to use as the guess?

 

[rock.freak667]

when you solved the auxilary equation if one root was 0, then for a polynomial, the particular integral would be a degree higher. For example if you solved and 0 was a root of the aux. eq'n. and the right side was ax+b, then the PI would be Ax^2+Bx+C

 

[lurflurf]

It is easy to know what to guess.
[D^2+2^2]cos(2x)=0
[D^2](4x+1)=0
Guess the solution to lcm{[2D^2+D],[D^2],[D^2+2^2]}=[D^2][2D+1][D^2+2^2]