I'd really love your help with the following exercise.
I need to show that if $y_1, y_2, y_3$ are particular solutions of the linear equation:
$y'+a(x)y=b(x)$, so the function $$\frac{y_2-y_3}{y_3-y_1}$$ is constant.
I got that a particular solution should be of the form: $e^{-\int_{x_0}^{x}a(s)ds}c(x)$, where $c'(x)=e^{\int_{x_0}^{x}a(s)ds}b(x)$. what else should I do? How should I solve this one?
Thanks!