1. The given compound is ethylamine-like formula:

$C_2H_7N$

2. Compare it with the general products in Duma's method:

$C_xH_yN_z + \left(2x+\frac{y}{2}\right)CuO \to xCO_2 + \frac{y}{2}H_2O + \frac{z}{2}N_2 + \left(2x+\frac{y}{2}\right)Cu$

3. Match atoms from $C_2H_7N$ with the general formula:

• Number of carbon atoms $= x = 2$
• Number of hydrogen atoms $= y = 7$
• Number of nitrogen atoms $= z = 1$

4. Therefore,

$y = 7$

5. Quick verification by substitution:

$C_2H_7N + \left(2(2)+\frac{7}{2}\right)CuO \to 2CO_2 + \frac{7}{2}H_2O + \frac{1}{2}N_2 + \left(4+\frac{7}{2}\right)Cu$

This is consistent with the general Duma's method expression.

Hence the required integer is:

$\boxed{7}$