My answer is:

[tex]

\frac{dc_A}{dt}= - 2 k_{1} \cdot ( c_A)^2 \cdot (c_B) \\

[/tex]

[tex]

\frac{dc_B}{dt}= - k_{1} \cdot ( c_A)^2 \cdot (c_B) \\

[/tex]

[tex]

\frac{dc_C}{dt}= - 3 k_{1} \cdot ( c_A)^2 \cdot (c_B) \\

[/tex]

I could be wrong.

As promised, I will attempt an abstraction. aA+bB+cC

dD+eE+fF (I may not write all 6 ODEs), order is x wrt A, y wrt B, z wrt C.

[tex]

\frac{dc_A}{dt}= - a k_{1} \cdot (c_A)^x \cdot (c_B)^y \cdot (c_C)^z \\

[/tex]

[tex]

\frac{dc_B}{dt}= - b k_{1} \cdot ( c_A)^x \cdot (c_B)^y \cdot (c_C)^z \\

[/tex]

[tex]

\frac{dc_C}{dt}= - c k_{1} \cdot ( c_A)^x \cdot (c_B)^y \cdot (c_C)^z \\

[/tex]

[tex]

\frac{dc_D}{dt}= d k_{1} \cdot ( c_A)^x \cdot (c_B)^y \cdot (c_C)^z \\

[/tex]

[tex]

\frac{dc_E}{dt}= e k_{1} \cdot ( c_A)^x \cdot (c_B)^y \cdot (c_C)^z \\

[/tex]

The important thing to note is:

[tex]

\frac{dc_{Species}}{dt}= v_{Species} \cdot k_{1} \cdot ( c_A)^x \cdot (c_B)^y \cdot (c_C)^z \\

[/tex]

Where v

_{Species} is the stoichiometric coefficient on that species in the reaction, multiplied by -1 if the species is a reactant and +1 if the species is a product.

The equations apply regardless of the values of x,y,z, including when they equal 0?