Exact solutions of a third-order ODE from thin film flow using X-symmetry method

We obtain exact implicit solutions of the third order ordinary differential equation y" =y(-n) for the first time. These exact solutions are obtained using X-symmetry reduction method, when n=(5/2) and n = (5/4). The obtained solutions are valid for the general initial conditions y(a) = gamma ,...

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Bibliographic Details
Published in:International journal of non-linear mechanics 2013-10, Vol.55, p.147-152
Main Authors: Abdel Kader, A H, Abdel Latif, M S, Nour, H M
Format: Article
Language:English
Subjects:
Contact angle
Differential equations
Exact solutions
Initial conditions
Mathematical analysis
Nonlinearity
Reduction
Thin films
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Summary:We obtain exact implicit solutions of the third order ordinary differential equation y" =y(-n) for the first time. These exact solutions are obtained using X-symmetry reduction method, when n=(5/2) and n = (5/4). The obtained solutions are valid for the general initial conditions y(a) = gamma , y'( alpha ) = delta , y"( alpha ) = beta . It is shown that the contact angle phi =90 degree when n = (5/2), and it varies with the initial conditions when n = (5/4).
ISSN:0020-7462