...parameters become absolutely constant and no envelope exists. The partial differential equation Rr+Ss+ Tt+ U(s"-rt) = V is remarkable also as including all the...the above method. First Investigation, 2. PROP. I. lfu=f(v] oe a first integral of the equation Rr+Ss+Tt+U(s*-rt)=F (1), then will u and v, considered...

...order admits a first integral of the form M and v being definite functions of x, y, z,p, q, and f(v) arbitrary in form. Neither of these statements is...remarkable law of reciprocity with the above method. ART. 2.] OF THE SECOND ORDER. First Investigation. 2. PKOP. I. lfu=f(v) le a first integral of the...

...first order and first degree, two of which systems are irrelevant and the other two relevant; Srdly that the solution of the two relevant systems ultimately...the above method. First Investigation. 2. PROP. I. 1fu—f(v) be a first integral of the equation Rr+Ss+Tt+U(s*-rt)=V. ........... (1), then will u and...

...first order and first degree, two of which systems are irrelevant and the other two relevant; Srdly that the solution of the two relevant systems ultimately...deduced independently of the assumption above mentioned. I shall also discuss the theory of the second integration. And I shall exemplify another method of...

...XIX, on the existence theorems, is exceedingly well done. First comes the proof of the existence of a solution of a system of ordinary differential equations of the first order and of a similar system of partial differential equations, the method being that of power series and fonctions...