# Tagged Questions

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

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### DSolve documention on web differs greatly from distributed MMA 10.2.0 version

In the course of improving my answer to 95361, I noticed that the DSolve documentation on the web is much better written than that distributed with Mathematica ...
111 views

### Trying to model a chemical reaction - NDSolve::litarg error

I am trying to model a chemical reaction with NDSolve. I have specified the known differential equations and parameters, ...
81 views

### DSolve gives an empty solution set to a solvable ODE

I really hope this isn't a duplicate, today I was answering this question and was to lazy to solve the quadratic equation on my own and so just asked mathematica to give me the solution of the ...
240 views

### Plotting a Bifurcation diagram

I have the following system equation v'(t)=2*G*J1[v(t-τ)]cos(w*τ)-v(t) How do you plot the bifurcation diagram, τ in the x ...
34 views

### Paramtric plot for 3 variable system

I have an system where I have calculated migration of "i" number of species "c" in "j" different habitats as a function of time. ...
46 views

### WhenEvent stops working after first instance

I'm modelling a very simple physical situation is which an object is rested on two moving fingers. Sometimes the object moves with one finger while sliding over the other, while at other critical ...
63 views

### Solving coupled ODEs with NDSolve to fit experimental data

I need to fit a multi-exponential data (Intensity x Time) using a model consisting of three differential equations. I want to find the parameters that gives the best fit to the experimental data. ...
40 views

### Recursion Depth Error when trying to solve a Differential Equation [on hold]

I'm trying to solve the equation $2x^{2}y''+(\sin x)y'-(\cos x)y=0$. After doing some scratch work I've come to the conclusion that I should be able to solve the equation with some code I've created: ...
44 views

### Specific explicit Euler question [on hold]

In my example I have the following differential equation: $y'(t)=t^2-2y(t)$. Given a fixed step size of $h=0.1$ and $y(0)=0$ and the condition $t\gt0$ I calculated the following values using the ...
64 views

### NDsolve complicated function

I'm trying to solve a complicated second-order ODE with NDSolve. I've never used NDSolve before. I've looked a lot of forums and tried some things, but I haven't been able to get the ODE's solution. ...
55 views

### Problems with multidimensional system of ODEs

I am trying to look at the migration of "i" number of species "c" in "10" number of habitats {designated as "j"} and to study their population size as a function of time "t". I have this following ...
32 views

### NDSolve::ndode: Input is not an ordinary differential equation [on hold]

I am new to Mathematica. I am working on solving the following different equations numerically written in the code as below. ...
69 views

### DSolve gives no output

I have troubles finding a solution to a system of three coupled nonlinear ODEs. When I put it into Mathematica, I get back the input as an answer. Could anyone tell me what I'm doing wrong? Here is ...
74 views

### Singularity problem of a 2nd order differential equation

I would greatly appreciate your help in implementation of Mathematica for solving a 2nd order differential equation expressing some important engineering problem. Apparently, this equation has no ...
171 views

### How to change symbols in differential equation with a single rule?

Problem Suppose I have a differential equation such as $\qquad f'(x)+f(x)=0$ and I want to change it into $\qquad y'+y=0$ My Method Using ...
92 views

### Heat transportation equation

I have a problem with the solution of the heat transportation partial differential equation in cylindric coordinates. Basically I have to numerically solve the equation for a pipe through wich the ...
39 views

### Error in NDSolve while differentiating a function dependent upon two variables [closed]

I want to differentiate a function dependent upon two variables, but my code gives an error: b1[m_, S_, t_, X_] := BesselY[0, [Beta][m]S[X, t]] Integrate[R*BesselJ[0, [Beta][m]*R]^2, {R, S[X, t], ...
62 views

### how to write generic equation for Recurring differential equations?

Hi I am a biologist and I want to model some ecological data that I have. I am new to mathematics and to ODEs. I want to write generic equations for a multi-dimensional system of ODEs. So, I want to ...
65 views

### Problem in solving a simple Laplace equation

I am trying to solve the following Laplace PDE in MMA: $$\frac{\partial^2 T}{\partial x^2}+\frac{\partial^2 T}{\partial z^2}=0$$ subject to the boundary conditions: \frac{\partial T}{\partial ...
38 views

### Diagonalisation of equations for NDSolve

I have a linear matrix differential equation and I wish to speed up evaluation by diagonalising using eigenvectors. There is an example in Help for finite elements under "swinging beam" that is ...
74 views

### Solving of three non-linear simultaneous differential equations with given boundary conditions

I am trying to solve three simultaneous differential equations in Mathematica-10 but I am not able to get the solutions. After running the following command as I am pressing shift+enter it just simply ...
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### Finding equilibria to a system of 3 ODEs with 11 unknown parameters. Looking for the intersection of 3 surfaces

I have the following system of 3 ODEs of 3 variables $(\ell,M,h)$ and 11 parameters $(\sigma_{\ell},\mu_{\ell},d_{\ell},\sigma_M,\alpha_1,\beta,\alpha_2,\nu_M,\sigma_h,\nu_h,d_h)$: ...
32 views

### Using BSpline as initial condition in NDSolve

I have not been successful in extending a 3D noise initial condition to a 2D situation. I would like to use a "noisy" initial condition to solve a non-linear PDE as shown. I used the following ...
81 views

### Why does Mathematica Hold my DSolve?

In one cell, I have ...
161 views

### ODE w/seasonal forcing term

I am working my way through a mathematical modeling book, and I'm having trouble replicating one of the results. The Differential equation is given as: $\frac{dC}{dt} = \frac{F}{V}(C_{in}-C)$, where ...
64 views

### How to specify a NeumannValue in a system of non-linear partial differential equations?

I am trying to solve a nonlinear system of partial differential equations. If I assume DirichletConditions it all works well. ...
115 views

### Differential equation solution

DSolve[y''[x] + (a - (b*x^2 - c)*x^2)*y[x] == 0, y[x], x] I couldn't solve this equation, please help
67 views

### How to rescale the independent variable? [closed]

I use NDSolve to solve several differential equations (same equation, but different defined constants) and then to plot the results. The dependent variable in my ...
195 views

### “Unstable” solution of a system of two coupled first order ordinary differential equation

Sorry for the long post. Maybe some of you will read the first few lines and already figure out what's going on, but in case it's not the case, I wanted to give as many details as possible. I came ...
76 views

### numerical integration of equation obtained by ParametricNDSolve

I am trying to find a definite integral of the solution obtained using ParametricNDSolve (i.e. y[x,a,b]) from 0 to 1 and plot ...
153 views

### Plot of the Mod of NDSolve solutions sometimes connects discontinuous jumps

UPDATE: The answers given are informative, and provide a workaround which has been given in other posts, but is unfortunately not very efficient. There still seems to be a lack of deeper understanding ...
265 views

### Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)

On this Mathematica.SE form, there exists information on how to use Mathematica to demonstrate the vibration of a circular membrane and the deflection of an orifice plate (the latter I had raised ...
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### Time evolution of a bispinor [duplicate]

The effective Hamiltonian for polariton graphene is given by: ...
116 views

### How to plot multi-colored regions separated by InterpolatingFunction on sphere

I would like to plot a sphere with multi-colored regions separated by solutions of a differential equation (no explicit expression is available for the separating curves). The result I am after would ...
45 views

### NDSolve emits CoefficientArrays::poly error [duplicate]

I'm trying to numerically solve a reaction diffusion equation in Mathematica, but I'm having trouble with the syntax. When I type in the following code, I get the error below it. I think it might have ...
78 views

### Backward in time numerical integration with fixed time step

Consider simple use of NDSolve[] function used to solve an ODE backward in time ...
113 views

### Wave equation with piecewise initial condition

I am trying to solve numerically the wave equation with the following initial and boundary conditions: ...
50 views

### NDSolve error in Mathemtica v10, but not v7 [on hold]

I have system of PDEs that are solved in NDSolve in Mathematica v7 (32bit) without any problem. When I try and run the code in version 10 (64 bit), it sometimes ...
60 views

### How to include the radiation from a surface in a heat flow PDE?

I have a PDE were the temperature distribution T[t,x,y] is to be determined. The region is a cross section of a (glass) plate. On one side I heat using a Neumann condition, on the opposite side I want ...
110 views

### What is the meaning of the error message “Set::write: Tag Plus in … is Protected”? [closed]

i'm trying to solve system of 9 coupled linear differential equations.I've this problem ... what is it's meaning?
85 views

### Iterating FindRoot to solve a differential equation

I am new to Mathematica style programming, better at traditional programming. I would like to know if I can create a table of results using FindRoot, where the ...
121 views

### Help nedeed for understanding NDSolve architecture -Vacuum Heating Simulation

I am a beginner in mathematica and I am facing a problem that is way bigger than my knowledge.. I am tryng to simulate a semplificated version of Brunel Effect, wich is a Laser-Plasma interaction ...
44 views

### Getting ALL solutions of the logistic ODE with DSolve?

In Mathematica 10.0, the command DSolve[y'[x] == y[x]*(1 - y[x]), y[x], x] gives {{y[x] -> E^x/(E^x + E^C[1])}} I take ...
119 views

### Coupled differential equations from Lagrangian — singularity being reached very quickly

I was wondering if there was a way to help the solutions to these differential equations not hit a singularity as quickly as they currently do. The equations are very complex (derived from a ...