Geodesic
A~necessary and sufficient condition for nonoscillatory behavior of the solutions of a~system of two linear equations of the first order
Matematičeskie zametki, Tome 16 (1974) no. 2, pp. 259-265.

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For the system $y'=b(x)z$, $z'=-a(x)y$, where $a(x),b(x)\in C(x_0,+\infty)$, $b(x)\ge0$ we obtain for $x\ge x_0$ a necessary and sufficient condition for nonoscillatory behavior. From this condition we derive new criteria for the nonoscillatory behavior of the system considered. 
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     author = {I. V. Kamenev},
     title = {A~necessary and sufficient condition for nonoscillatory behavior of the solutions of a~system of two linear equations of the first order},
     journal = {Matemati\v{c}eskie zametki},
     pages = {259--265},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a9/}
}
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I. V. Kamenev. A~necessary and sufficient condition for nonoscillatory behavior of the solutions of a~system of two linear equations of the first order. Matematičeskie zametki, Tome 16 (1974) no. 2, pp. 259-265. http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a9/