The organic compound that gives a positive Tollens' test and reacts with 2,4-dinitrophenylhydrazine suggests the presence of an aldehyde. The product formed with hydroxylamine would be an imine derivative, corresponding to the reaction of the aldehyde with hydroxylamine. Hence, the correct product is \(\text{CH}_3\text{CH}_2\text{NOH}\), ethylhydroxylamine.