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.
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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MHB First order differential equations
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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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MHB Writing PDE in terms of x and y
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I PDEs greater than order 2 with real world applications?
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MHB -b.1.3.17 y''+y'-6y=0 Find values of r of the form y = e^{rt}
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MHB -b.1.1.4 directional field as t \to \infny
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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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MHB How do we choose this function?
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I Where does the "i" go
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MHB -b.1.3.12 .... is a solution of the DE
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MHB -b.2.7.2 Euler's method y'=3+y-y y(0) =1
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I Understanding relationship between heat equation & Green's function
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MHB -b.2.2.24 separate variables
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I Finite difference scheme for u'=u^2, u0=1, 0<t<2
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MHB -t1.13 IVP \frac{ds}{dt}&=12t(3t^2-1)^3 ,s(1)=3\
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MHB B.2.2.16 IVP of \dfrac{x(x^2+1)}{4y^3}, y(0)=-\dfrac{1}{\sqrt{2}}
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MHB -2.1.1 DE Find the general solution
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I General solution of heat equation?
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MHB -b.2.1.15 ty'+2y=t^2-t+1 IVP
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MHB -b.1.3.10 Verify the following given functions is a solution of the differential equation
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I Solve second order linear differential equation
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MHB 2.1.2 Find the general solution of y'−2y=t^{2}e^{2t}
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I Conservation of finite difference for vibration equations
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MHB -2.2.35 Show that dy/dx=(x+3y)/(x-y) is homogeneous. and....
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B Difference between a continuously differentiable function and a wave
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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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MHB Solving an ODE: Seeking c so y'(0)=0
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A Starting BDF iterations - suggestions?
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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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MHB B.2.1.4 trig w/ integrating factor
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MHB Solving $\dfrac{dy}{dt}=y-5$, $y(0)=y_0$
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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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MHB B.1.2.3 Find the equilibrium solution and....
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MHB B.1.3.7 Solve IVP
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MHB -b.1.3.18 >values of r for de
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A Phase Portraits of a system of differential equations
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MHB -a.8.5.99 Solve system
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I Independent Variable Change
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B Real world applications of differential equations
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MHB -7.1.8 IVP with system of eq
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MHB 3.4.5.5 solve IVP
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A Is a solution of a differential equation a function of its parameters?
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MHB -a.3.2.97 second order IVP
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MHB -1.5.7.9 find gereral solution to DE
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MHB Solving a Differential Equation
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MHB -1.8.17 initial value then find C
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I 9-point Laplacian stencil derivation
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A Implementing FDM Boundary Conditions at a Red Point
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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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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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