Question

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 don't get that...i got this answer from the back of the book but i am trying to understand it...please help if possible...

Answer 1

plz someone help me...if anyone knowssssssss

Answer 2

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.