An account of singular solutions of differential equations of the first order is given in every text-book on differential equations. The theory of singular solutions of differential equations of higher order is not usually given in elementry treatises. It is discussed by Goursat (American Journal of Mathematics, xi., pp. 329-372), who bases his discussion on the theory of singular solutions of simultaneous equations ot the first order. From the didactic point of view a more elementary treatment may be acceptable, and an attempt is here made to indicate how singular solutions of a given equation of the second order may be found by simple means.