On approximate solutions of a class of Clairaut's equations

M. Onitsuka and Iz. El-Fassi

It is well known that Clairaut’s equation can be solved, but its perturbed equation cannot. In addition, Clairaut’s equation has two interesting properties: it has a singular solution and no uniqueness of the solutions. This study overcomes these difficulties and analyzes the error between the approximate and exact solutions of Clairaut’s equation. Moreover, it contains important ideas as an approach to differential equations which have non-unique solutions. Examples and numerical simulations are given to understand the results.

Applied Mathematics and Computation

428

127205

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https://doi.org/10.1016/j.amc.2022.127205