What is wrong with my work? please,check
Use variation parameters to find particular solution for x"+x=cost, x1=cost, x2 =sint

Question

What is wrong with my work? please,check
Use variation parameters to find particular solution for x"+x=cost, x1=cost, x2 =sint

loser66 · Answer

Thanks @Big_Mensa961  but I got it now.

dinamix · Answer

$$x"+x=0 => r^2+1=0 => r^2=-1 =>r^2=\pm i$$

radar · Answer

If $$r ^{2}=-1$$

radar · Answer

How does $$r ^{2}=\pm i$$
also ??

dinamix · Answer

ops i made mistake $$r=\pm i $$ ty @radar

dinamix · Answer

the complete integral of corresponding  equation homogeneus x''+x =0 is : $$X=acost+bsint$$ 
and the particular solution the nonhomogneus and since the i is a simple root of the auxiliary equation i seek the paritcular solution in the form $$x* =t(Acost+Bsint)$$
and put this solution and romplace it in this $$x''+x=cost$$ and find A and B 
(A not equal a not same that also for b)
the general solution is :
$$x=X+x*$$

dinamix · Answer

cuz i found A=0 and B=1/2 when i remplace it @wio  could u check the my solution for this equation $$x"+x=cost$$ i solve it look up

dinamix · Answer

$$x= acost+bsint+\frac{ 1 }{ 2 }tsint$$

dinamix · Answer

@IrishBoy123  could u see my solution for him

irishboy123 · Answer

that seems to be the right answer :-)) https://www.wolframalpha.com/input/?i=x%22%2Bx%3Dcost