Solving first order linear differential equations With a chemical reaction $A + 2B → 3C$, concentrations $a (t)$, $b (t)$ and $c (t)$ of the three substances A, B and C in the differential equations satisfy: 1. $ \frac {da} {dt} = -rab^2$ 2. $\frac{db}{dt} = −2rab^2$ 3. $\frac{dc}{dt} = 3rab^2$ Show that for every $t$, $b (t) - 2a (t) = 0$ and $c (t) + 3a (t) = 3$? I never studied about this kind differential equations nor i find any source anywhere, how do i solve this?

There is no need to actually solve the DE's.

Notice that $$2a'=b'$$ So $$b'-2a'=0$$ Integrating with appropriate boundary conditions, $$b-2a=0$$

Same goes for the second equation, since $$c'+3a'=0$$