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 Determining equilibrium solutions to differential equations
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I The constant value on the given exact differential equation
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Insights Differential Equation Systems and Nature
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I Cylindrical coordinates -Curvilinear
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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 When Lie Groups Became 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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I Derivation for the indicial exponent in the Frobenius method
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Differentiation of unitary operator U(t,t') in Peskin and Schroeder
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I Solving 3D TDSE with Runge-Kutta Method
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A Seeking advice about solving an ODE
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I What kind of differential does the small Greek delta letter represent?
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A How to separate variables in this PDE?
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I Understanding Euler Method: Finding Initial Condition of y(0)=1
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I Laplace Transform of Sign() or sgn() functions
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I PDE - Heat Equation - Cylindrical Coordinates.
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I Helmholtz Equation in Cartesian Coordinates
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A Solving an Equation: Overcoming the r's
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I Finding the weak form of an eq. with DG elements (finite elements)
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A Clarification on the given PDE problem
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A The boundary conditions in reference to Laplace's equation
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A Applying the Laplace transform to solve Differential equations
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I Explanation of all "its linearly independent derivatives"
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B Differentiating Euler formula vs. multiplying by i
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A Solve the Partial differential equation ##U_{xy}=0##
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A Determining whether the Dirichlet problem is nonhomogenous
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I Need Help with this Step in a DE solution
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A Rectangular higher order edge element (finite element method)
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MHB Volterra-Lotka system.
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B Solving Kepler's 1st law as a function of time
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I Discontinuous systems? And why do we need uniqueness anyway?
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I Where did this substitution technique go wrong?
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I Expressing a differential equation into a different format
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I Can we solve a non-autonomous diffeq via Taylor series?
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I What are the applications of function-valued matrices?
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A How to solve Diffusion Equation with time dependant conditions?
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I Second order non-homogeneous linear ordinary differential equation
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A Polar Fourier transform of derivatives
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I Function min and max help
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A Spectral solution of the two dimensional Rossler chaotic system
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I Can I Solve y in y^2=ln(1-y^2)?
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I Understanding Removable discontinuity of the given function: ##e^x##
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A Solve the heat equation having Dirichlet boundary conditions
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I Second Order ODE with Exponential Coefficients
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I Analysis of converting a DE into complex DE
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A Solve the homogenous Neumann problem
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A Bessel functions of imaginary order
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I Hypergeometric Limits: Analyzing p(x)
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A When should you use more mesh elements in the finite element method?
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I General solution of 1D vs 3D wave equations
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I Real ODE yields real solution through complex numbers
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I Quick Change of Variables Question
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I Drawing Direction Fields for Higher Order ODEs
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MHB Interpreting a proposition
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MHB Inexact Differential Equation with 4 Degree
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MHB Sturm-Liouville Problem Cheat Sheet
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MHB Bessel Functions Cheat Sheet
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A Recurrence relations for series solution of differential equation
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I FEM Method in 2D with Triangular Elements
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I How to make the deflection equation at any point along a snow ski profile?
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MHB Matrix Methods for Difference Problems II
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MHB Matrix Methods for Difference Problems
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MHB S9.3.a de with u subst
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I Differential Equations For Solving A Recursive equation
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I Modified Bessel Equation
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Differential Equations

Welcome to the Differential Equations forum!

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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