# Questions tagged [differential-equations]

Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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### How to return only the negative complex solutions of DSolve or using FindInstance

I am using DSolve to find the solutions to two differential equations. The problem is from the first solution, I only want the solution that includes a negative ...
1 vote
71 views

### Post Processing of Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain

Linked Question: Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain.II Many many thanks to @Nasser (https://mathematica.stackexchange.com/users/70/nasser) for his ...
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### Stiffness or singularity in NDSolve for a system of equations with switchpoint

I am trying to solve the following set of equations: ...
100 views

### Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain.II

This question is connected with reference to my previous question (Solution of Dimensionless Partial Differential Equation Over a Semi-Circular Domain), where I asked for a help to solve the following ...
1 vote
48 views

### Why this code does not show three legend lines?

My code shows empty legend lines. What should I do to show the graph with three legend lines? ...
1 vote
98 views

### NDSolveValue result contradicts initial condition

I'm trying to solve the Schroedinger equation in a box with two holes defined by: ...
166 views

### Plot general solutions

Is it possible to plot the general solutions of the following pde: ...
1 vote
79 views

### A way to generalize my code for this non linear ODE problem

I am trying to solve the differential equation $y''(x) = y(x)+\sin[y'(x)]$ using "Fixed Point Iteration" over the interval $[0,1].$ Now using central difference method I arrived at the ...
1 vote
58 views

### Adding symbolic functions and manipulating results of DSolve

I want to add a symbolic function and its second derivative. The symbolic function is given by DSolve: ...
207 views

### Solution of Dimensionless Partial Differential Equation Over a Semi-Circular Domain

My problem is to solve the following BVP. and I want to recreate a contour plot like the following graph using Mathematica. I am trying with the following code. ...
122 views

### Solve Differential Equation Numerically

I investigated my system and encountered differential equation such as $y''(x) = e^{y(x)}-e^{-2y(x)}-e^{y(x)-y(x+d)}$, where $d$ is a constant. The boundary condition is $y'(0) = 30$ $y'(\infty)=0$. I ...
1 vote
78 views

### Solve dimensionless PDE in polar coordinate over a semi-circular re

I am trying to solve the following BVP in mathematica using the following code: ...
1 vote
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+500

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### Solving differential equation with hyperbolic functions

I've been trying to solve the following differential equation: \begin{equation}\left( \frac{d \tau}{d \sigma} \right)^2 = \frac{(E_0 \cosh\sigma-p_\tau\sinh\sigma)^2}{(E_0 \cosh\sigma-p_\tau\sinh\...
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### Why does DSolve show result as {}? [closed]

Using the following code, I get as an output: {}. Does anyone know what does that means? ...
1 vote
80 views

### Axisymmetric cylindrical Laplace's equation with a boundary condition at infinity

I'm trying to solve Laplace's equation in cylindrical coordinates. The solution is axisymmetric and also symmetric with respect to the $r=0$ plane. Hence I only care about solving in one quadrant. The ...
38 views

### Plotting NIntegrate result obtined from NDSolve

I am trying to get a plot of x vs dpdx when - 0.5 < x < 0.5 which uses the results of NDsolve and F vs delp when -2<F<2. ...
155 views

### How to numerically solve symmetric top with fixed point motion equations with Mathematica?

I am trying to numerically solve the equations associated with the motion of a symmetric top with a fixed point. Details about this system can be found in Goldstein's Classical Mechanics book (3rd ...
1 vote
38 views

### Is there documentation for "FeynmanKacFormula" under "ItoProcess"? [closed]

Under the command ItoProcess there are "Properties related to ItoProcess" and one is "FeynmanKacFormula". Where can I find documentation on this?...
57 views

### Plot several graphs of a function density distribution using Table

I would like to plot the density distribution graphs of the eigenfunction en[B][[2, 1]] when a parameter B is changed. But the ...
114 views

### Second order Poisson ODE

I have a 2nd differential Poisson equation for the electric field in a semiconductor (application for a MOS simulation, hopefully). I have the formula: with the condition that after a certain value(...
1 vote
78 views

### NDSolve problem with conservation laws

I am not an experienced Mathematica user, but decided to use it this time because of the in-buit special functions that it has. My problem is a solution of the following ODE ...
34 views

### ParametricNDSolve with known solution at one limit

The ODE I wish to understand is the following: ...
78 views

### Need help solving cylindrical Laplacian

I'm trying to solve the cylindrical Laplacian for a heated disk in a large cylinder. The cylinder and disk have constant temperatures and I only care about the temperature field between the disk and ...
44 views

### ODE of HJB function

I want to solve the following ODE where W is a function of x. Any suggestion? Thank you! ...
100 views

### How do I get a coefficient matrix from a second order ODE's system?

I got this system: I need to transform this ODE system in a matrix form, because I need to evaluate its stability and, further, plot the eigensystem with the Stream Plot function. Is there any ...
60 views

### Plotting phase portrait for second order ODE(which has no analytical solution)

I'm trying to plot $y(t)$ against $y'(t)$ (phase portrait) for the following ODE: $$y''(t) + y(t)+9.8*sgn(y'(t))=0$$ where all derivatives are with respect to $t$. Due to the presence of the ...
42 views

### WhenEvent in ParametricNDSolve but not executed

I tried to solve a partial differential equation with parameters, the critical condition of which I used WhenEvent to express, but the solution after bringing in the parameters shows that the ...