Geodesic
Stability on the basis of Orthogonal Trajectories
Canadian mathematical bulletin, Tome 8 (1965) no. 5, pp. 647-658

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We consider a system of differential equations of second order given by 1 (' = d/dt) where P and Q have continuous first partial derivatives with respect to x and y in some open and simply connected set R containing O = (0, 0) which we assume to be the only singular point in R. In fact, let R be the whole plane; for if not then the following discussion can be modified. 
Burton, T. A. Stability on the basis of Orthogonal Trajectories. Canadian mathematical bulletin, Tome 8 (1965) no. 5, pp. 647-658. doi: 10.4153/CMB-1965-048-8
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     title = {Stability on the basis of {Orthogonal} {Trajectories}},
     journal = {Canadian mathematical bulletin},
     pages = {647--658},
     year = {1965},
     volume = {8},
     number = {5},
     doi = {10.4153/CMB-1965-048-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-048-8/}
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