Math Help - particular solution of high order 2d

1. particular solution of high order 2d

y'''' -6y'''+9y''=x

i take y_p=ax+b

i get 0=x

so i cant find the a ,b for the solution

2. Originally Posted by transgalactic
y'''' -6y'''+9y''=x

i take y_p=ax+b

i get 0=x

so i cant find the a ,b for the solution

$r^4-6r^3+9r^2=0 \iff r^2(r-3)^2$

so the complimentary solution already contains $y=ax+b$

Since there is a factor of $r^2$ you must multiply your guess by $x^2$ to get $ax^3+bx^2$

3. what are they laws tieing the homogeneus and the practical solutions?

i we have also (r-3)^2 thing
why its not changing the particular solution too
?

whats the general theory on think link thing
?
i dont know how to search it on google

4. Try this link, it may help.

The Method of Undetermined Coefficients

Also try google Method of undetermined coeffients.