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Summary:
A practical problem leads to the investigation of a system of equations in the form $f(x,y,y',z)=0$. The well-known theorem on the solvability of the system of equations in the form $f(x,y,y',z)=0$ applies also to the above system. The condition that the Jacobian $\bold J=\partial t/\partial(y',z)$ is nonzero is, under the corresponding assumptions, sufficient for the existence of a solution $(y(x), y(x))$ of the system. Further the necessity of this condition is proved if the functions $z(x)$ and $y(x)$ are required to be respectively once and twice continuously differentiable. The presented theorem may be applied in mechanics as well as in the theory of electric circuits with concentrated parameters.
References:
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[3] Jiřina M.: Solvability of the equations of the networks with lumped general variable parameters. Information processing machines Sborník VÚMS, č. 20, 1973.
[4] Jiřina M.: Řešitelnost rovnic nelineárních obvodů sestavených metodou uzlových napětí. Elektrotechnický časopis č. 1, 1972. MR 0388614
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