# Questions tagged [differential-equations]

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

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### “Fewer dependent variables than equations, so the system is overdetermined” without any BC's

Consider this system of PDEs. eqn1 = D[u[x, t], x] + 5 D[u[x, t], x, x] + D[v[t], t, t] - 4 == 0 eqn2 = D[v[t], t] + D[u[x, t], t, t] + v[t] == 0 I would like to ...
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### Solving Laplace's equation in 2D using region primitives

I was looking at examples of solving problems in electromagnetism and ran across this question, which was a great example of just that. However, looking at the Dirichlet condition, both answers define ...
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### NDSolve with Events that reevaluate with different Discrete Variables

I have the following problem: I have a set of ODEs and some discrete variables which I can solve successfully. Now I want mathematica to check at every $0.1 \,t$ time step, wether it would increase ...
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### A system of linear differential equations with variable (time-dependent) coefficients

I have searched almost all similar pages discussing a system of differential equations, but none of them discussed the case of variable coefficients. My problem is a bit more complicated, because ...
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### find ODE solutions and suitable initial conditions to get solution

DSolve[2.56 x''[t] == -0.32 x'[t] - x[t] - 0.05 x[t]^3 + 2.5 Sin[t], x[t], t] I want to find the solution and ﬁnd two initial conditions such that their ...
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### How to get DAE representation from equations?

Update2: Thank you for all of your answers. I would like to clarify the question as I did a bit of research on DAE representations and their applications in software. There are 2 representations used ...
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### 2D Oseen equations

Background info: https://en.wikipedia.org/wiki/Oseen_equations ...
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### Parametric plot of data from NDSolve

I have been trying to plot the solution of a set of differential equations solved used NDSolve. Now, in one of the cases, I have the find a parametric plot of the ...
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### NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two

I was in the impression that V12 can now handle higher order PDES but for this particular case it fails to produce any solution. ...
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### Plot a family of solutions of ODE with singularity

In the post Use Mathematica to plot the flow of an ODE with discontinuity, the following ODE with discontinuous coefficient was solved ...
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### Delay in the beginning of solution for two ODEs

I have two couple ODEs and the second one has a delay in the time for starting. I mean, the first ODE starts at t=0 and the second one at t=20. How can I solve the second one in the correct time ...
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### How to use Parallel computing on Manipulate option on ParametricNDSolveValue

My aim is to use Manipulate option on the ParametricNDSolveValue. When ever i run my code "Manipulate" option runs very slow and some time shows Aborted when check for that value of parameter it works ...
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### Solving ODEs vs VoronoiMesh

I'm using VoronoiMesh to model cells in an epithelium. The concentration of certain proteins within the cells are determined by solving a system of ODEs per cell. ...
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### 1d coupled field PDE in MMA

how can we correctly solve 1d coupled field pde in MMA 12? Description for the problem: the article the phase field fracture model in one dimension I have proposed the following code (based on the ...
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### NDSolve and DSolve solutions

Sorry for this probably trivial question, but I'm at a loss with this simple problem and the way Mathematica handles it. It's about a free-falling object, dropped by a height of 10, starting with zero ...
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### I can't get DSolve to work on coupled equations

In trying to solve a geodesic equation, I have these coupled equations: ...
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### Singularity in my system of differential equations causing problems for NDSolve

I have the following differentials equations, with the corresponding initial conditions: ...
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### Deep learning outperforms in symbolic integration and ODE?

There comes a new paper on arXiv (arXiv 1912.01412, Deep Learning for Symbolic Mathematics by Guillaume Lample, François Charton) claiming that a deep learning model outperforms Mathematica a lot in ...
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### How to help NDSolveValue handle the addition of another dependent variable in a set of reaction-diffusion equations

I am trying to use NDSolveValue to solve a system of coupled reaction-diffusion equations in a 2D space (technically 3D cylindrical coordinates, but due to radial ...
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### System model merge with multiple input and one output

I was curious, and I used the built-in functions of Mathematica to analyze the following scheme: I used SystemModelMerge as: ...
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### Using Grad and NDSolve with vector variables

A simple orbital model might be developed like this: ...
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### NDSolve Stiffness and Strange Behaviour with Dirichlet Conditions

I working with the following semiconductor potential equilibrium equation for a diode $$\psi(x)''=e^{\psi(x)}-e^{-\psi(x)}+10^6\text{sgn}(x-(l+r)/2)$$ where $l$ and $r$ are left and right boundaries ...
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### solve a differential equation numerically

I have to solve numerically an equation of the form ...
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### How to solve ode with convolution?

my question is as this and i want to get the solution of this ode x(t) \$ ({M_{33}}{\rm{ + }}{{\rm{m}}_{33}})x''(t) + \int\limits_{ - \infty }^t {x'(tau){K_{33}}(t -...
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### Phase portrait of n-dimensional state-space system

It is usually not difficult to study the state space for n = 2,3 variable states. What if these variables are more than 3, for example 4,5 or 6? There is a rule according to which the dynamic features ...
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### solve a matrix differential equation numerically [closed]

I want to solve numerically a differential equation like iy'[t]=y[t]/20 where y is a 2*2 matrix and i is iota. Please suggest me a way to proceed.