IMCS/Publications/BASM/Issues/BASM n.3 (31), 1999/

On applications of Riemannian geometry in theory of the second order ordinary differential equations. (English)

Authors: Driuma Valeriu


Some properties of Riemannian and Einstein-Weyl spaces associated with the second order nonlinear differential equations $y''+a_{1}(x,y){y'}^3+3a_{2}(x,y){y'}^2+\mathbreak+3a_{3}(x,y)y'+a_{4}(x,y)=0$ with arbitrary coefficients $a_{i}(x,y)$ and dual equations $b''=g(a,b,b')$ with function $g(a,b,b')$ satisfying the partial differential equation $g_{aacc}+2cg_{abcc}+2gg_{accc}+c^2g_{bbcc}+2cgg_{bccc}+ g^2g_{cccc}+(g_a+cg_b)g_{ccc}-4g_{abc}-\mathbreak -4cg_{bbc} -cg_{c}g_{bcc}- 3gg_{bcc}-g_cg_{acc}+ 4g_cg_{bc}-3g_bg_{cc}+6g_{bb} =0$ are considered.

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