Show that the solutions of the differential equationare the two families of curves xy= A and x^2-y^2= B. Show that these two sets of curves are orthogonal trajectories. 相关知识点: 试题来源: 解析 when xy=Ay-A/x, y-A/xA((A^2)/(A^2^2))-(x^2-(A^2)/(x^2))4/(x^2)-...
By looking at the interaction between coefficients and solutions within the setting of families of differential equations in the unit disk, we obtain sharper results than were found in the setting of one differential equation. Specifically, we consider normal families, within both analytic and ...
find the value of the number a such that the families of curves y = (x+c)^-1 and y = a (x+k)^(1/3) are orthogonal trajectories
In this thesis we consider the problem of computing the zeta function and the number of rational points of an algebraic curve over a finite field. More precisely, we study this problem for nondegenerate curves, a very general class of curves containing for example all elliptic, hyperelliptic an...
Affine lines in the complement of a smooth plane conic We classify closed curves isomorphic to the affine line in the complement of a smooth rational projective plane conic Q . Over a field of characteristic zero, we show that up to the action of the subgroup of the Cremona group of the ...
We construct the largest dimensional family of nodal degree d hypersurfaces in \mathbf {P}^{2n+2} with positive defect for d sufficiently large.Similar content being viewed by others On the irreducibility of the Severi variety of nodal curves in a smooth surface Article 06 June 2019 A ...
If one has a more specific Banach space {\mathcal {C}} with additional properties, then \theta -curves of maximal slope satisfy differential inclusions. The following result is a simplified and slightly modified version of [1, Proposition 1.4.1] and is stated in terms of the duality mapping...
Ramanujan, in his lost notebook, gave an interesting identity, which generates infinite families of solutions to Euler's Diophantine equation A3+B3=C3+D3. In this paper, we produce a few infinite families of solutions to the aforementioned Diophantine equation as well as for the Diophantine equa...
wherezis the propagation distance,xis the transverse coordinate, andgis the strength of the Kerr nonlinearity. Replacingzby timet, Eq. (1) may be used as the GP equation for the BEC wave function, with the effective mass affected by a nonuniform optical lattice72. In the spatial-domain opt...
Elliptic families of solutions of the Kadomtsev–Petviashvili equations and the field elliptic Calogero–Moser system, Funk. Anal. i Prilozhen - Akhmetshin, Krichever, et al. () Citation Context ... branched covers of elliptic curves. This approach is extended in [Kr3], where the elliptic ...