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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L
I How to solve this second order differential equation
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dextercioby
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Resources for self-studying PDEs.
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A Phase Portraits of a system of differential equations
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193
wrobel
I Independent Variable Change
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178
P
B Real world applications of differential equations
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152
H
A Is a solution of a differential equation a function of its parameters?
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3
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140
jedishrfu
I 9-point Laplacian stencil derivation
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12
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614
Paul Colby
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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9
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317
Paul Colby
I How to solve this BVP
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5
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334
Chestermiller
I Why is this differential equation non-linear?
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12
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423
D
A Solution of nonhomogeneous heat equation problem
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6
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285
Shackleford
A Example of Ritz method with Bessel functions for trial function
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5
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229
joshmccraney
I Solving and manipulating the damped oscillator differential equation
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6
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308
vela
A Causality in differential equations
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6
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2K
M
A Laplace eq. in cylindrical coordinates and boundary conditions
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177
P
I Understanding the change of variables for PDEs
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210
Isaac0427
I An interesting Nonlinear Differential Equation
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12
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465
Isaac0427
A Green's Function half-space
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135
Shackleford
A Estimates on derivatives
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184
Shackleford
What are the limitations of the Explicit Finite Difference Model?
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319
F
What is the relation between stability criterion and time step?
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222
Filip Larsen
I How to solve f'(t) = -t + t^3.f(t)
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5
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447
H
I How does one solve Uxx+Uyy+Uzz=C when C is non-zero?
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1K
BvU
A Improper boundary in non-linear ODE (pseudospectral methods)
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225
Leonardo Machado
I How to solve this vibration equation?
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14
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823
Delta2
I Solving a system of differential equations by elimination
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4
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330
Mark44
I The diffusion equation with time-dependent boundary condition
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8
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519
C
A Non linear diff. eq. first order
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12
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492
anuttarasammyak
I Problem with checking solution by wolframalpha
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4
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202
Infrared
I Deep Learning the new key to nonlinear PDEs?
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2
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554
wrobel
I Is it possible to solve such a differential equation?
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20
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665
R
I Problem with checking the solution to a differential equation using WolframAlpha
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4
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278
P
I Justification (or philosophy) of modal analysis
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3
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258
Ssnow
A Generic Solution of a Coupled System of 2nd Order PDEs
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2
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358
wrobel
I Using v substitution for first order homogenous DE and constraining solution
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4
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315
Mayhem
I Sure way to convert variable integral to infinite integral?
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10
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467
P
I Quasilinear Equation but with non-zero initial condition?
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3
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965
P
I PDEs cracked by Artificial Intelligence at Cal Tech
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345
L
A Modal Analysis vs. the Solution to the Diff.Eqs.
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341
T
I Non-linear ODE: initial conditions
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324
fresh_42
I Integrating with the Dirac delta distribution
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9
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744
vela
A Solution to an ODE (Leaky Integrate and Fire Neuron Model)
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8
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571
M
A Going to higher degrees to obtain other solutions?
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608
jk22
I Chain Rule and acceleration as a function of two variables
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F
I Transforming Cartesian Coordinates in terms of Spherical Harmonics
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388
E
I Did von Neumann coin the eth or dyet for the inexact differential?
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6
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429
nomadreid
A Nonlinear Wave Equation (Nonlinear Helmholtz)
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395
Fred Wright
I Derive local truncation error for the Improved Euler Method
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520
P
I Assuming boundary conditions when integrating by parts
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366
martinbn
I ODE solution question
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jim mcnamara
I Separation of Variables and Integrating over an Interval
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332
vela
I Laplace transform linearity problem
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549
P
I What is the nth derivative of this equation?
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Neothilic
I The Trapping Region of the Lorenz equations
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571
O
I Fourier Integral of the Schrodinger Equation
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627
Charles Link
A Solving a differential equation with two unknowns
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394
M
A Separation of variables possible in this problem?
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434
P
A Inhomogeneous wave equation: RHS orthogonal to homogeneous solutions
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443
J
B Wave equation with a slight alteration
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hutchphd
A Eigenvalue problem: locating complex eigenvalues via frequency scan
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13
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662
joshmccraney
A Boundary conditions in the time evolution of Spectral Method in PDE
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552
joshmccraney
I Know a simple, linear, complex, eigenvalue BVP?
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3
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339
joshmccraney
Equation satisfied by a rubber sheet
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24
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Steven van Dokkum
I Heat transfer coefficient and convection
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3
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585
fluidistic
I Vector space for solutions of differential equations
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424
martinbn
A Question about this Separable ODE statement in a book
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8
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637
SchroedingersLion
A Solution to a differential equation with variable coefficients
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457
bigfooted
A Differential Equations (Control Optimization Problem)
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418
A
I Differential equation with two terms
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410
K
I Poisson's inhomogeneous PDE and its solutions
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684
F
I Boundary Conditions For Modelling of a Fluid Using Euler's Equations
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16
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831
person123
A Numerically calculating the solution for a non-homogeneous ODE system
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6
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Leonardo Machado
ODE -> Transfer Function Assistance
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2
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406
BlueTempus
I Vibration Problems -- Why must there be two solutions to the DE?
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19
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T
I What is a modal analysis?
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397
Paul Colby
A Crank-Nicholson solution to the cylindrical heat equation
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23
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Chestermiller
I Looking for help with this PDE
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5
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417
C
A Numerically solving matrix Riccati ODE
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3
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454
bigfooted
A Numerical Solution to Random Linear Non-Homogeneous ODE
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Avatrin
A Partial Differential equation (Heat eqn)
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664
martinbn
B Complete set of solutions to the wave equation
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393
hutchphd
Solving a System of PDE's Using Maple
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G
I Solving the Wave Equation via complex coordinates
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883
jk22
I Alternating Direction Implicit method for solving 2D Heat diffusion
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564
Vick
I Solving a DE for modelling the spread of an infectious disease
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5
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704
Chestermiller
I Thermodynamics Differentiating logarithms
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H
I Deriving the differential equation for the underdamped case
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483
Tony Hau
A Partial differential equation containing the Inverse Laplacian Operator
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3
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wrobel
A Identifying and solving a pair of ODE's
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6
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603
Milsomonk
A 11 coordinate system for separation of variables
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4
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F
I How to solve this non separable ODE?
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jk22
A Rational Chebyshev Collocation Method For Damped Harmonic Oscilator
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2
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562
Leonardo Machado
A Is this a known result? (hypergeometric function at special values)
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5
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728
N
I Phase Plane Diagram w/ Complex eigenvalues
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joshmccraney
B Predator-prey model of a virus
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18
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D
A Crank-Nicholson method and Robin boundary conditions
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8
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H
I Bernoulli Equation with weird integral
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705
H
I Help getting started with this differential equation
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H
I Constants in DE's
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Mark44
I PDEs: Laplace's Equation over a Parallelogram
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J

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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