Represent the following families of curves by forming the corresponding differential equations (a being parameter): (i)(x−a)2−y2=1(ii)x2+y2=ax3 View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, ...
The differential equation of family of curves whose tangent form an angle of pi/4 with the hyperbola xy=C^2 is
Differential Equations Find the differential equations of the following family of curves. 1. Parabolas with axis parallel to the y – axis with distance vertex to focus fixed as a. 2. Parabolas with axis parallel to the x – axis with distance vertex to focus fixed as a. 3. All ellipses...
H. Movasati, S. Reiter, Painlev´e VI equations with algebraic solutions and family of curves, Journal of Experimental Mathematics, Vol. 19, Number 2 (2010), 161-173.H. Movasati and S. Reiter. Painlevé VI equations with algebraic solutions and family of curves . Journal of Experimental...
To find the orthogonal trajectories of the given curve first, we differentiate the given family of curves with respect toxon both sides and find the slope of tangent. Therefore the slope of the perpendicular tangent (orthogonal) is the negative reciprocal that is−1dydxSolve it differential eq...
In this paper we deal with the following problem: given an algebraic plane curve C, implicitly defined, we determine its "asymptotic family ", that is, the set of algebraic curves that have the same asymptotic behavior as C.(c) 2022 The Author(s). Published by Elsevier B.V. This is ...
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate-Shafarevich group for descent via Richelot isogeny. We prove this by performing a descent via Richelot isogeny and a complete 2-descent on the isogenous Jacobian. We also give an explicit...
13). Cyclic DSC curves of ZW-UiO-67·MSA (within 0 ~ 150 °C) show two exothermal events respectively at 114 and 95 °C during cooling (Fig. 2a, Supplementary Fig. 5b), while a Tg onset appears at 104 °C in the following up-scan. No Bragg diffraction found for a...
The differential equation of the family of curves y=ex(Acosx+Bsinx), where A and B are arbitrary constants is (a) (b)(c)(d)(e)(f)d(g)2(h)(i)yj((k)d(l)x(m)2(n)(o))(p)(q)−2(r)(s)dyt((u)dx)(v)(w)+2y=0(x) (y) (z) ( a a ) (bb) (cc)(( d d...
The large sieve, monodromy and zeta functions of curves version of a result of Chavdarov on the "generic" irreducibility of the numerator of the zeta functions in a family of curves with large monodromy.doi... Kowalski,E - 《Journal Für Die Reine Und Angewandte Mathematik》 被引量: ...