Let $(E)$ : $a(x).y'+b(x).y=\phi(x)$ \ such as $a$ and $b$ are two continuous functions, verifies $a(x),b(x)≠0 : x\in \mathbb{R}^+$
Let $S$ be the solution set of $E$. Is $S$ a VECTOR SPACE ?
My answer : If $\phi(x)=0$, then $S$ will be a vector space. but what if $\phi(x)≠0$, or in this case we can just say that $S$ is infinite ?