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

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0
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1answer
52 views

How to obtain coefficients after solving differential equation of order 2 with initial condition?

I have the following answer of a differential equation of order two ...
0
votes
0answers
43 views

Strange difficulty with DSolveValue

Consider: sys = {u (1 - u + a v), r v (1 - v + b u)} (* {u (1 - u + a v), r (1 + b u - v) v} *) And: ...
2
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0answers
79 views

Axes in a vector plot

Consider: ...
3
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1answer
258 views

How I can make the StreamPlot of this differential equation?

I need the StreamPlot of this differential equation but I don't know how. dp/dt = 0.4 p(1 - p/30), 0 <= t < 5 and 0.4 p (1 - p/30) - 0.25 p, t > 5
1
vote
2answers
204 views

How can I create function which contains an ODE system and its numeric solution?

I have created a function like the following, which contains an ODE system. And I want to know the effect of different parameters. ...
1
vote
1answer
62 views

Plotting 2nd order ODE solution for specific values of constants

Suppose that I have a 2nd order, linear ODE and I want to plot the solution I found using DSolve. How can I plot giving specific values of ...
0
votes
1answer
78 views

Problems with DSolve [closed]

I'm trying to solve and plot a second order ODE. Here is my code: DSolve[y''[x] + 4 y'[x] + 12 y[x] == 80 Sin[2 x], y[x], x] Problem 1... it sticks me with a ...
0
votes
1answer
69 views

Plot an ODE solution for a list of specific constants [closed]

Let's say I have a 1st order ODE and want to plot the solution. What I have been doing until now is: ...
6
votes
2answers
497 views

Plotting separatrices for nonlinear system

Consider the system: \begin{align*} x'&=(1-x-y)x\\ y'&=(4-7x-3y)y \end{align*} The system has a saddle point at (1/4,3/4). How can I plot the separatrices on the phase portrait having domain ...
6
votes
2answers
349 views

Kernel quits without error in NDSolveValue

The crash is fixed in version 10.3 I am using the latest 10.1. The following single line command makes the kernel quit without error message (just a beep): ...
24
votes
1answer
1k views

Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
1
vote
1answer
139 views

Error with using NDSolve [duplicate]

I am currently trying to numerically solve a system of differential equations. Here is my code: ...
0
votes
1answer
71 views

Boundary condition not correctly imposed for NDSolve

I notice that when plotting the below NDSolveValue ...
2
votes
0answers
153 views

Failing to solve a simple PDE with NDSolve

I'm trying to solve the following PDE. Actually this is a major simplification of the original with all x,z dependent coefficients being fixed. For some reason Mathematica (10.0) cannot solve even ...
1
vote
1answer
178 views

Solving coupled differential equations with an eigenvalue

I have 2 coupled differential equations with an eigenvalue Ei and want to solve them ...
0
votes
1answer
180 views

Eigen energies of 2D time independent Schrödinger equation

Firstly, I am aware that a similar question of this type was asked, but it was not helpful as it was only one dimensional (so please don't mark my question as a duplicate) The trouble I am having is ...
0
votes
1answer
234 views

Time evolution of a wave packet from the time-independent Schroedinger equation [duplicate]

Starting off with the time-independent Schroedinger equation (TISE) $\quad \quad -\frac{\hbar^2}{2m} \nabla^2 \psi + V(r, \theta) \psi = E\, \psi,$ I would like to study the time evolution of an ...
0
votes
1answer
72 views

NDSolveValue with Map

I have: ...
4
votes
1answer
267 views

NDSolve to solve a PDF

I would like to solve numerically the following PDE: $$ \frac{\partial}{\partial t} p(x,t)=-\frac{\partial}{\partial x}p(x,t)+\frac{1}{2}\frac{\partial^2}{\partial x^2}[x^2\,p(x,t)],\;x\ge0,\;t\ge0, ...
0
votes
0answers
61 views

Integro differential eq boundary difficulties

I'm trying numericaly solve simple integro-differential equation, but have some problems with boundary conditions. System: ...
1
vote
1answer
100 views

Why NDSolve cannot solve such a simple set of differential equations? [closed]

I want to solve a set of ODE like below, but Mathematica outputs nothing for this which greatly confused me. WHY? ...
-3
votes
1answer
94 views

How to draw phase portrait graph for nine system of differential equations in mathematica? Can have a code for darwing this? [closed]

The differential equations for the transmission dynamics of HIV/AIDS are given as follows: ...
0
votes
2answers
75 views

Integrating ODE's

I have: $$ m\frac{dV_y}{dt}=-k\cdot V_y-mg $$ where, $V_y$ is velocity in the $y$-direction. I have the initial condition Vy[0]=40 Sin[40 Degrees] and ...
0
votes
2answers
103 views

Problems solving/plotting a differential equation

I am trying the following: Plot[DSolve[{1220*x''[t] + 1000*x'[t] + 35600 x[t] + 4500*x[t]^3 + 2135 == 0, x[0] == 0, x'[0] == -5}, x, t], {t, 0, 10}] Could ...
7
votes
1answer
192 views

Detecting nearly simultaneous WhenEvents in NDSolve

I am trying to solve a system of (many) coupled nonlinear ODEs. I need to decouple some of the equations (i.e. set the time derivatives of some of the dependent variables to zero) at various points in ...
2
votes
0answers
58 views

Update NumericalFunction in NDSolve

I have NDSolve` StateData from an NDSolve` ...
0
votes
1answer
136 views

How to adjust excel data for NonlinearModelFit?

I'm really new to Mathematica and I'm facing a problem and would really appreciate some help! Maybe my question is similar to one described in How to fit 3 data sets to a model of 4 differential ...
2
votes
4answers
359 views

Solving differential equation

I want to solve the following differential equation DSolve[y''[x] == (λ y[x])/Sqrt[-1 + x], y[x],x] But do not know how to actually solve it. Any suggestion?
0
votes
1answer
182 views

NDSolve::bcedge: Boundary condition not specified on a single edge

NDSolve::bcedge: Boundary condition c[t,5]==Cout is not specified on a single edge of the boundary of the computational domain. >> I'd like to plot $\frac{\partial}{\partial ...
0
votes
0answers
89 views

DSolve response with DSolve

I'm trying this code ...
0
votes
1answer
141 views

Using WhenEvent

I want to solve this simple equation with a event: ...
1
vote
1answer
123 views

Solving ODES in order to find unknown constants

I am trying to solve a set of ODES which represent a second order consecutive chemical reaction. ...
0
votes
0answers
91 views

How to sweep a parameter in an ODEs system using ParametricNDSolveValue?

I want to analyze how my ODEs system behaves when I change only one parameter (in this case d). ...
0
votes
0answers
153 views

Solving a big System of ODEs

I want to solve numerically a linear first-order ODE system with over 12000 equations. I used NDSolve with implicit options: ...
0
votes
1answer
197 views

NDSolve solving problem

I am trying to solve for the function y[x] obeying the ODE: $ \frac{x}{1 + x}y^{\prime\prime}(x) + \frac{2 x + 1}{(1 + x)^2} y^{\prime}(x) = \frac{1}{3\sqrt{y(x)}} ...
2
votes
2answers
441 views

Solve ODE in State-space form

Is it possible to solve an ODE in state-space form in mathematica? Such as x'[t]=A.x[t] I attempted ...
1
vote
1answer
210 views

Forcing solutions to avoid Root[]

I'm solving a system of ordinary non-homogeneous differential equations (4 equations). The solutions will include some algebraic equations solutions as known from text books due to the use of an eigen ...
2
votes
2answers
165 views

Exact Differentials

I just started using Mathematica so my apologies if this is a very basic question. I tried to find related questions on this forum but couldn't, so here goes. I have an equation, $\quad \quad dp ...
0
votes
1answer
139 views
1
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0answers
75 views

How to plot three related differential equations in Mathematica? [closed]

Eq1: $ \frac{1}{3\phi}=\left[\frac{x}{x+1}\frac{d^{2}}{dx^{2}}+\frac{2x+1}{(x+1)^{2}}\frac{d}{dx}\right]{\phi^{2}} $ Eq2: $ ...
0
votes
1answer
164 views

How can I create a phase plane? [duplicate]

I want to make a phase plane for an equation system. I want it to look something like a Mu-Space in Stat-Mech. Basically I want it to show the same system with various different initial condition ...
1
vote
4answers
262 views

How can I remove horizontal lines on a phase plot for a pendulum?

I am attempting to do a phase plot for a driven,damped pendulum. When the angle wraps from Pi to -Pi or -Pi to Pi I get a horizontal line on the plot. I would like to remove these lines as they mask ...
5
votes
1answer
238 views

NDSolve and FEM support for non conformal meshes of a disk [with Kernel crash]

I want to create an ElementMesh for a disk. For my specific scenario, some author advise to use a regular mesh, where the radial and tangential directions are ...
1
vote
1answer
156 views

Poisson PDE in a rectangular domain

I found a solution for this problem, but this is in Scilab and I never use Scilab. Can anyone can help me to translate it in Mathematica? Here is the Link:http://imechanica.org/files/TorqueR.pdf I ...
0
votes
0answers
90 views

Trying to plot solution curves on top of a direction field

I'm trying to do some diff. eq. homework that requires taking a general solution to a differential equation and graphing a series of possible solution curves over a direction field of the general ...
7
votes
3answers
242 views

Vector form using NDSolve

Michael E2 wrote a wonderful solution for my question. Now I am considering the system: $$ \begin{align*} x'&=x^2 y,\ x(0)=1\\ y'&=-x y^2,\ y(0)=1 \end{align*} $$ I am wondering how I can ...
4
votes
1answer
148 views

NDSolve Poisson PDE for rectangle with hole

When I solved the Poisson PDE with function NDSolve in a rectangular domain with hole in the center, and search the first derivative with x and y why appear these protrusions on the diagram around the ...
0
votes
0answers
457 views

Laplace PDE in a polar coordinate system

I want to solve a Laplace PDE in a polar coordinate system with finite difference method, but I have a problem with boundary conditions at r = 0. Here is what I ...
2
votes
1answer
284 views

NDSolve for axisymmetric problem

I would like to solve an axisymmetric Poisson equation on a disk with FEM. The code for Cartesian coordinates works fine: ...