NONLINEAR DIFFERENTIAL EQUATIONS AND ALGEBRAIC SYSTEMS

In this paper we obtain the general solution of scalar, first‐order differential equations. The method is variation of parameters with asymptotic series and the theory of partial differential equations.The result gives us a form like a differential quotient requiring only that a limit be taken. Like...

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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences 1978, Vol.1978 (3), p.257-267
Main Author: Williams, Lloyd K.
Format: Article
Language:English
Subjects:
Abel equations
Cauchy-Kowalewski system
Cauchy-Kowalewski theorem
Riccati equations
universal Cauchy-Kowalewski system
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Summary:In this paper we obtain the general solution of scalar, first‐order differential equations. The method is variation of parameters with asymptotic series and the theory of partial differential equations.The result gives us a form like a differential quotient requiring only that a limit be taken. Like the familiar expression for the solution of linear, first order, ordinary equations, it is the same in all cases.
ISSN:0161-1712
1687-0425
DOI:10.1155/S0161171278000290