Ordinary Differential Equations
44 questions across 2 topics. Also examined in CNET.
General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's Function
- 62ODE — Abel's formula gives W(1)=e, not an optionMSET June 2025General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 64ODE — stability of constant-coefficient equationsMSET June 2025General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionMedium
- 61Euler equation — no value of K actually gives c1+c2ln xMSET April 2024General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionHard
- 86Solutions of a y"-dependent functional form a four-parameter familyMSET April 2024General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionMedium
- 62A shared zero forces the Wronskian to vanish identicallyMSET March 2023General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionMedium
- 63Differential equation of a family of circles centred on the x-axisMSET March 2023General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 67Orthogonal trajectories of a parabola familyMSET March 2023General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 82The brachistochrone's defining first-order ODEMSET March 2023General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 85Euler equations for a two-variable parametric functional, combined into a 4th-order ODEMSET March 2023General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionMedium
- 33Abel's formula — no y' term means a constant WronskianMSET September 2021General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionMedium
- 34Solving xy'=2y and tracking a specific solution curveMSET September 2021General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 35Eliminating both constants from y=ae^bxMSET September 2021General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 86Eigenfunctions for distinct eigenvalues are never linearly dependentMSET September 2021General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionHard
- 34Solving x,dy-y,dx=0: the family of lines through the originMSET December 2020General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 35Clearing a fractional power before reading off the degreeMSET December 2020General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 84A fourth-order Euler–Poisson equation solved exactly by sin xMSET June 2019General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionMedium
- 94Laplace transform of a repeated-root second-order IVPMSET June 2019General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 47Damped oscillations come from characteristic roots -alphapm iomegaMSET January 2018 Paper IIGeneral Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 48Abel's formula: W=Ce^-a1tMSET January 2018 Paper IIGeneral Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 50A linear homogeneous fourth-order equation has a four-dimensional solution spaceMSET January 2018 Paper IIGeneral Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 44X(0)=0, X'(1)=0 picks sinsqrtlambda,t with cossqrtlambda=0MSET January 2018 Paper IIIGeneral Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
- 46Independence can be lost on a subinterval — but not for solutions of a linear ODEMSET April 2017 Paper IIGeneral Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionMedium
- 48Power series: 2C2=-C0 from y"=-e^xy at x=0MSET April 2017 Paper IIIGeneral Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionEasy
Existence & Uniqueness, Singular Solutions, Systems of First Order ODEs
- 61ODE — eliminating a constantMSET June 2025Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 63ODE — a Lipschitz constant on a rectangleMSET June 2025Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 65ODE — the logistic equation tends to its stable equilibriumMSET June 2025Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 66ODE — integrating factor e^x^2MSET June 2025Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 67ODE — a linear combination that decouples the systemMSET June 2025Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsMedium
- 63Series solution — the printed key does not match the recurrenceMSET April 2024Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsHard
- 77Picard's method — the first successive approximationMSET April 2024Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 79Runge–Kutta order 4 — identifying the K3 stageMSET April 2024Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsMedium
- 65Picard's existence interval, optimised over the rectangle's heightMSET March 2023Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsMedium
- 69Cauchy problems for a PDE can have no, one, or infinitely many surfacesMSET March 2023Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsMedium
- 90Converting x"-x=0, x(0)=1,x'(0)=1 into a Volterra equationMSET March 2023Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 87Converting a trivial IVP into a Volterra integral equationMSET September 2021Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 91RK2 (Heun's method) for a single stepMSET September 2021Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 34Solving a Bernoulli equation via the substitution v=1/yMSET June 2019Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 67Uniqueness for the wave equation's Cauchy problemMSET June 2019Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 91One step of Euler's methodMSET June 2019Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 49(My-Nx)/N=2x depends on x alone: integrating factor e^x^2MSET January 2018 Paper IIExistence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 46Eliminate a using x-a=2y/y'MSET January 2018 Paper IIIExistence & Uniqueness, Singular Solutions, Systems of First Order ODEsMedium
- 47The equation is exact: d(x+ye^x/y)=0MSET April 2017 Paper IIExistence & Uniqueness, Singular Solutions, Systems of First Order ODEsMedium
- 48y1^2-y2^2le2by1-y2 needs yle bMSET April 2017 Paper IIExistence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy
- 47frac ddt(x^2-y^2)=2xy-2yx=0: hyperbolasMSET April 2017 Paper IIIExistence & Uniqueness, Singular Solutions, Systems of First Order ODEsEasy