Competitive Stats

Partial Differential Equations

45 questions across 3 topics. Also examined in CNET.

Practise Partial Differential Equations Filter in the bank

Lagrange and Charpit Methods, Cauchy Problem for First Order PDEs

68PDE — surfaces orthogonal to xyz=cMSET June 2025Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
69PDE — data on a characteristic curveMSET June 2025Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
70PDE — uniqueness of general and complete integralsMSET June 2025Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
71PDE — characteristic curves and envelopesMSET June 2025Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
72PDE — integrability of Pfaffian equationsMSET June 2025Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
74PDE — envelope of planes through the originMSET June 2025Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
69The PDE of every surface of revolution about the x-axisMSET April 2024Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
71Envelope of a family of unit spheres — the characteristic is a great circleMSET April 2024Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsHard
72Naming the arbitrary-function solution of a first-order PDEMSET April 2024Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
68The characteristics of yp-xq=0 are exactly the shared intersection circlesMSET March 2023Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsEasy
70A transversal curve gives a unique paraboloid of revolutionMSET March 2023Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
72Integral surfaces and characteristic curves — a two-way theoremMSET March 2023Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
74Pfaffian and Lagrange normals describe the same surfacesMSET March 2023Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
31Eliminating two constants from z=ae^bxsin(by) — Laplace's equation appearsMSET September 2021Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
31The defining PDE for axial symmetry about the z-axisMSET June 2019Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
46Integrability of a Pfaffian equation: XcdotcurlX=0MSET January 2018 Paper IILagrange and Charpit Methods, Cauchy Problem for First Order PDEsEasy
47Lagrange's method: xy and x^2+y^2+z^2 are first integralsMSET January 2018 Paper IIILagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
48Coefficients of zx,zy involving z make the PDE quasi-linearMSET January 2018 Paper IIILagrange and Charpit Methods, Cauchy Problem for First Order PDEsEasy
49z=ae^bxsin by is harmonicMSET April 2017 Paper IILagrange and Charpit Methods, Cauchy Problem for First Order PDEsEasy
50Check the complete integral: p=2a/(z+b), q=2/(z+b)MSET April 2017 Paper IILagrange and Charpit Methods, Cauchy Problem for First Order PDEsMedium
44Eliminating f from z=f(x^2+y^2+z^2)MSET April 2017 Paper IIILagrange and Charpit Methods, Cauchy Problem for First Order PDEsEasy
45A product pq of derivatives makes equation (ii) non-linearMSET April 2017 Paper IIILagrange and Charpit Methods, Cauchy Problem for First Order PDEsEasy
46Orthogonal surfaces: z(3z+1)(p+q)=x+y, through the given circleMSET April 2017 Paper IIILagrange and Charpit Methods, Cauchy Problem for First Order PDEsHard

Separation of Variables (Laplace, Heat and Wave Equations)

Classification of Second Order PDEs