Consider the differential equation
$$y''+5y'=-sin(x)-1$$ Find the general solution.
Here's my work: I found the solution to the homogeneous equation to be: $y_h(x)=C_1e^{-5x}+C_2$
And for the particular solution, I guessed
$y_p(x)=Acos(x)+Bsin(x)+C$
$y_p'(x)=-Asin(x)+Bcos(x)$
$y_p''(x)=-Asin(x)-Bcos(x)$
After I plugged everything back into the differential equation, I got
$(5B-A)cos(x)-(B+5A)sin(x)=-sin(x)-1$
What should I do with the constant $-1$?