# particular solution of high order 2d

• Dec 8th 2010, 07:25 AM
transgalactic
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
• Dec 8th 2010, 07:40 AM
TheEmptySet
Quote:

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

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

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

Since there is a factor of \$\displaystyle r^2\$ you must multiply your guess by \$\displaystyle x^2\$ to get \$\displaystyle ax^3+bx^2\$
• Dec 8th 2010, 11:08 AM
transgalactic
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
• Dec 8th 2010, 02:23 PM
TheEmptySet
Try this link, it may help.

The Method of Undetermined Coefficients

Also try google Method of undetermined coeffients.