We Know that if
$$ax'' +bx' + cx = g(t)$$
We have to find the solution of homogeneous case $x_h(t)$ and a particular solution $x_p(t)$. So the general solution will be
$$x(t) = x_h(t) + x_p(t)$$
But, I saw that if $g(t)= d$ is constant, then the general solution is
$$x(t) = x_h(t) + d$$
I dont understand it. It is true?
If it is not true, there is some way to find a particular solution more easy in case $g(t) = d$ constant?
May be, to make it clearer, considering $$ax'' +bx' + cx = d$$ let $$cx-d=y \implies x=\frac{y+d}c\implies x'=\frac{y'}c\implies x''=\frac{y''}c$$ Replace to get $$ay'' +by' + cy = 0$$