A problem on calculus and integration and need some clarification on that point

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So I have just started learning some calculus and I came across this problem. I have spent 1 hr on it and I haven't been able to come up with any idea so as to what is going on in this problem. I did expand it using Linear diffrential equation but after the integration, I could not understand what was happening.

I'd be glad if some one could tell me what is happening here. Please don't solve this. I just want to understand this problem. Is this related to increasing or decreasing functions?

Note: This is a multiple choice question!!!

Let $f,g:[0,\infty) \to \mathbb R$ be continous funtions.

Let h(x) be a solution of $\frac {dy}{dx} + f(x)\times y = g(x)$ with $h(0)=c$

And let $p(x)$ be a solution of $\frac {dy}{dx} + f(x)\times y ≥ g(x)$ with $p(0) = c$

then:

a) $p(1)≥h(1)$

b) $g'(x) +f'(x) > h(x)$

c) $g'(x) ≥ h(x)$

d) $f(x) +g'(x) < h(x)$