Linearization of Two Second-Order Ordinary Differential Equations via Fiber Preserving Point Transformations
Keyword(s):
The necessary form of a linearizable system of two second-order ordinary differential equations y1″=f1(x,y1,y2,y1′,y2′), y2″=f2(x,y1,y2,y1′,y2′) is obtained. Some other necessary conditions were also found. The main problem studied in the paper is to obtain criteria for a system to be equivalent to a linear system with constant coefficients under fiber preserving transformations. A linear system with constant coefficients is chosen because of its simplicity in finding the general solution. Examples demonstrating the procedure of using the linearization theorems are presented.
2010 ◽
Vol 15
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pp. 139-143
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2014 ◽
Vol 410
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pp. 341-347
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2005 ◽
Vol 461
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pp. 2451-2477
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Vol 465
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pp. 609-629
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2011 ◽
Vol 16
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pp. 3447-3450
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