Homework Help: grouping

Posted by mary on Wednesday, November 19, 2008 at 10:51am.

i am trying to solve for A and B....this question comes from a Differential equations...but this step goes back to basics...

Asinx-Bcosx+6Acosx+6Bsinx=3-cosx

when you group all the sinx and cosx
you get

(A+6B)sinx+(6A-B)cosx=3-cosx

you get

(A+6B)=0 and (6A-B)=-1<<<<<<<<<

i am having a hard time understanding the second part where i have the <<<< next to it...i mean shouldnt it be =-3 i really dont get that...i got this answer from the back of the book but i am trying to understand it...please help if possible...

PLZZZ - mary, Wednesday, November 19, 2008 at 11:59am
plz someone help me...if anyone knowssssssss
grouping - bobpursley, Wednesday, November 19, 2008 at 1:20pm
The point of what you are doing is finding a particular solution. Ignore the -3, get the like coefficents as in the text, solve for A,B. Then you go back and try the solution you found to see if it works in the differential equation. If it does, you are ok with a particular solution. If it does not, often that checking will suggest a modification to your solution. This method is not exact, it sometimes takes iterations.

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