Differential Equations Forum

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Join in expert discussion on differential equation topics like ODE and PDE. Differential equations are an equation involving derivatives of a function or functions.
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Intro. to Differential Equations
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I A question about variables of integration
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A About ellipticity and a proof that a system of PDEs is elliptic
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A Volterra equation of the second kind
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I Direction Fields and Isoclines
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A Should the boundary condition have to satisfy dimensional consistency?
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I Why Lagrange’s method of solving Pp + Qq=R works?
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A Show positivity and boundedness of a non-linear system
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A The heat equation for a composite having contact resistance
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I Visual Representation of Separation of Varables
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I Understanding Legendre differential equation
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I Proving a basis is a basis for homogeneous linear differential equation with constant (complex) coefficients
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A Searching for radial part solution of Klein-Gordon type equation
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I 1D time dependent PDE - using orthogonal collocation
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A Boundary conditions sufficient to ensure uniqueness of solution?
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B Mathematical equation of motion of a differential two-wheeled Sumo robot
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B Deriving an asymmetric logistic growth model
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A Solving for a steady-state (passive cable equation)
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I Stuck on solving a non homogenous (linear) PDE
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I Solving ODE with Laplace transform and Existence and Uniqueness Theorem
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A Symplectic split of Hamiltonian with complex term
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A Computing end-points using the Neumann condition
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A Need help with Rodrigues formula example in Riley, Hobson, Bence - Mathematical Methods for Physics and Engineering 3rd edition
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I When is an ODE (numerically) reversible in time?
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I Question about the general solution to Hooke's law
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I How to do Magnus expansion for time-dependent companion matrix?
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Request resources to understand Picard–Lindelöf for ODEs
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I Energy of moving Sine-Gordon breather
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I Runge-Kutta 4 w/ some sugar on the top: How to do error approximation?
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I Maxwell's equations PDE interdependence and solutions
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I Understanding the given transformation - PDE
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I A step in a proof of linear dependence of ODE solutions
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B Solving Kepler's 1st law as a function of time
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A Heat conduction equation in cylindrical coordinates
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A Circuit ODE with multiple short voltage impulses
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I Number of solutions to the order of the equation
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I Numerically solving a non-local PDE
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I Green's function for 2-D Laplacian within square/rectangular boundary
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I Toy problem to motivate the idea of advanced Green's functions
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I How to Solve a Nonlinear PDE with Sinh Function?
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A Navier-Stokes solutions: Beltrami flow
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I Detailed solution of an envelopes example in a math book
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General solution vs particular solution
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A A question about an 'extremal' surface
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Why is the Heat equation solved with separation of variables but not with Fourier transformations?
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I Uniform convergence of functions
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I On vibrating string and differentiating infinite sum
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I Determining the dimension of a given PDE
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I Navier-Stokes equation in a triangular coordinate system
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I Getting zeros and poles for Laplace transform
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I V * grad(V) = grad(V^2/2) - rotor(omega)
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A SDE valuation equation (stochastic calculus)
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Insights Differential Equation Systems and Nature
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I LIF Neuron Equation Solution for arbitrary time-dependent current (Neural Dynamics)
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I Determining linear indepedence/dependence of a set of functions
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I Reduction of order in solving second order differential equations
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I Heavyside’s operational calculus vs. transforms
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I How to Evaluate This Stochastic Expectation Value?
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I Differential equation using power series method
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I Find the directional derivative of ##f## at the given point
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I Determining equilibrium solutions to differential equations
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I Cylindrical coordinates -Curvilinear
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I The constant value on the given exact differential equation
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I Determining directional Field for say ##\dfrac{dy}{dx}=y-x##
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A Solve PDE w/ Comsol 5.3: Numerical Solution & Time Evolution
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A Discretisation of a PDE in Lagrangian coordinates
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I Good positing in electrostatics problem with dielectrics - Poisson problem with conditions at the Dirichlet or Neumann edge
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B Solving PDEs via FEM: A Gut Check of the Procedure
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I On a bijective Laplace transform
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I On Laplace transform of derivative
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A Legendre Polynomials -- Jackson Derivation
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B Incorporating boundary conditions in the Finite Element Method (FEM)
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I On sub and super solutions: Teschl and others
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A Integrability of Systems of Differential Equations
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I On the approximate solution obtained through Euler's method
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I On error estimates of approximate solutions
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I Feynmann's connection machine model
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I Verifying properties of Green's function
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I Question about solving linear first order non-homogeneous ODEs
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I Solving Differential Equation Using Reduction of Order
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A Stability analysis for numerical schemes of systems of PDEs
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A The field equations of elasticity
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I Heat Equation: Solve with Non-Homogeneous Boundary Conditions
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A Solving System of PDEs: Analytical Methods & Solutions
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I Solve Int. Eq.: Exponential Growth Diff. Eq.
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I "Rationale" for Homogeneous vs. Nonhomogeneous Differential Equations?
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A Obtaining a variable value from a 5-th degree polynomial in the tangent form
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A How to work around this equation giving infinities in the numerical calculation?
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I Finding the time for the first shock for a quasilinear first order PDE
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A Separation of variables is possible only in 11 coordinate systems?
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A Numerically solving a transport equation
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I What's the mathematics behind "spontaneous synchronization"?
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I Characteristic curves for ##u_t + (1-2u)u_x = -1/4, u(x,0) = f(x)##
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I Rosenbrock method ODE : Abrupt increase during First iteration
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A Differential equation and Appell polynomials
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I Solution of delayed forcing function
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I Infinite product representation of Bessel's function of the 2nd kind
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A Raising and lowering operators
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Insights How Did Lie Groups Become Central to Physics?
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I ODE with non-exact solution: closed-form, non-iterative approximations
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I Fundamental matrix of a second order 2x2 system of ODEs
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