Geodesic
The Heun Equation and the Darboux Transformation
Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 267-277.

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In this paper, we study the Darboux transformation of the Darboux–Treibich–Verdier equation. On the basis of this transformation, we construct a generalization of the Darboux transformation to the case of the Heun equation and to other linear ordinary differential equations of second order. Examples are given. 
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Yu. N. Sirota; A. O. Smirnov. The Heun Equation and the Darboux Transformation. Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 267-277. http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a9/

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