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 FEM Method in 2D with Triangular Elements
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I Differential Equations For Solving A Recursive equation
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I Modified Bessel Equation
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A Determining whether the Dirichlet problem is nonhomogenous
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Finding the damping ratio (zeta) of an nth order system from a transfer function
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I Converting Second Order ODE to Hypergeometric Function
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Derivation of Momentum Equation (Eulers Equation)
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A FEM basis polynomial order and the differential equation order
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Coupled First Order ODE
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I How to make the deflection equation at any point along a snow ski profile?
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A Wave direction and speed of propagation
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A How to work around equation giving infinities numerically
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I FEM in 2D Part II
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A How can I interpret the 2D advection equation?
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I Equations of motion for the Schwarzschild metric (nonlinear PDE)
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I FEM Method in 2D
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Insights The Amazing Relationship Between Integration And Euler’s Number
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A Lagrangian form of an equation
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I Looking for what this type of PDE is generally called
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A Finite difference scheme for y'(t)=a*y(t)
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A Crank-Nicholson method for spherical diffusion
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A The Kowalewskaya example
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A Green's function for Stokes equation
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A Green's function for Sturm-Louiville ODE
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A Residual of PDEs as convergence criteria of numerical solution
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A Residual of PDEs solved by FEA
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I Crank Nicolson method to solve a PDE
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I FEM Method for the Wave Equation
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I Limit cycles, differential equations and Bendixson's criterion
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I Inverting an Equation Containing Elliptic Integrals
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A Help with understanding why limit implies uniqueness
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I Separation of Variables, but not equal to constant
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I Laplace transform of a simple equation (Simple question)
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Dynamic Systems: Poincaré-Bendixson Theorem finite # of equilibria
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I Integral-form change of variable in differential equation
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A Solving Laplace's equation in polar coordinates for specific boundary conditions
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A Why do the Navier-Stokes equations give us non-existent results for 3D flow?
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A Laplace transform of derivatives
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A Existence of unique solutions to a first order ODE on this interval
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I Problem with integrating the differential equation more than once
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I Non-Homogeneous Robin Boundary conditions and Interpretations of Signs
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A Solving nonlinear singular differential equations
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When do we need to consider the homogeneous solution?
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I Can FDM solve any type of PDE same as FEM?
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I Find the center manifold of a 2D system with double zero eigenvalues
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A Dissipative and dispersive derivatives
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A Heat equation coarsened
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I Nonlinear differential equation
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I An equation invariant under change of variable
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I PDEs greater than order 2 with real world applications?
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A How to solve simple 2D space-time PDE numerically
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I How to determine if x(t) is a solution to a system x'(t)=f(x)
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I Where does the "i" go
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I Understanding relationship between heat equation & Green's function
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I Finite difference scheme for u'=u^2, u0=1, 0<t<2
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Differentiation of unitary operator U(t,t') in Peskin and Schroeder
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I General solution of heat equation?
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I Solve second order linear differential equation
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I Conservation of finite difference for vibration equations
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B Difference between a continuously differentiable function and a wave
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I Generation of a Gaussian a random process with Matlab
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B Basic Idea of Differential Equations
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A Local truncation error from Taylor/Variable timestep
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A Backward Euler technique vs. periodic function: Damping out?
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A Starting BDF iterations - suggestions?
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A Adding noise and solving stochastic ODEs in Python
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I Laplace Transform of cos(t)/t
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I Fredholm's alternative & L2 convergence
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I How do I solve this first order second degree differential equation?
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I Series Solution for 2nd-Order Homogeneous ODE
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I How to solve this second order differential equation
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A Phase Portraits of a system of differential equations
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I Independent Variable Change
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B Real world applications of differential equations
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A Is a solution of a differential equation a function of its parameters?
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I 9-point Laplacian stencil derivation
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A What is the boundary condition equation at the point interface of 3 areas in magnetostatics in Finite Difference Method (FDM)?
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I How to solve this BVP
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I Why is this differential equation non-linear?
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A Solution of nonhomogeneous heat equation problem
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A Example of Ritz method with Bessel functions for trial function
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I Solving and manipulating the damped oscillator differential equation
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A Causality in differential equations
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A Laplace eq. in cylindrical coordinates and boundary conditions
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I Understanding the change of variables for PDEs
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I An interesting Nonlinear Differential Equation
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A Green's Function half-space
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A Estimates on derivatives
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What are the limitations of the Explicit Finite Difference Model?
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What is the relation between stability criterion and time step?
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I How to solve f'(t) = -t + t^3.f(t)
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I How does one solve Uxx+Uyy+Uzz=C when C is non-zero?
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A Improper boundary in non-linear ODE (pseudospectral methods)
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I How to solve this vibration equation?
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I Solving a system of differential equations by elimination
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I The diffusion equation with time-dependent boundary condition
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A Non linear diff. eq. first order
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I Problem with checking solution by wolframalpha
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I Deep Learning the new key to nonlinear PDEs?
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I Is it possible to solve such a differential equation?
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Differential Equations

Generally, Differential equations are basis for every meaningful physical theory in existence. They are the starting point for the math. DEqs are the mathematical language to express how things change.

All of our physical observations are in the terms of how things change. If you translate the observed changes in the physical world carefully into mathematics you have a differential equation. Solve the differential equations and you have a tool to make a physical prediction.

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