an:01873303
Zbl 1058.53507
Lukashevich, N. A.; Chichurin, A. V.
To the theory of geodesic lines equation
RU
Nelinijni Kolyvannya 2, No. 1, 30-35 (1999).
00093001
1999
j
53C22 34A30
geodesic lines equation; general integral
The authors determine a class of geodesic lines equations whose general integral is
\[
\phi_3(x)=C_1\phi_1(x)\,\exp\lambda_1y(x) + C_2\phi_2(x)\,\exp\lambda_2y(x),
\]
where \(C_i\), \(\,i=1,2\), are arbitrary constants, \(\,\phi_i\), \(\,i=1,2,3\), are analytic functions \(\,(\not\equiv)\,\) and \(\,\lambda_1\) and \(\,\lambda_2\) are fixed constants. Also the Abel equation is considered. For this equation the conditions are established which ensure the integration in quadratures and the form of the general integral is shown.
A.~Ju.~Obolenskij (Ky??v)