# Questions tagged [differential-equations]

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

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### Optimal way to approximate initial condition for PDE?

I have a Fokker-Planck PDE \begin{align} \frac{\partial p}{\partial L}(L,\eta) = \eta^2\frac{\partial^2 p}{\partial\eta^2}(L,\eta) +(1-2\eta)\frac{\partial p}{\partial\eta}(L,\eta)+\frac{2(\eta-1)}{\...
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### NDSolve issue, potential singularity or stiff system

I have the following parameters, equations, and NDSolve solution set up as such: ...
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### Numerical Issues Using Results of NDSolveValue

I am solving Laplace's Eqn. (Cartesians) in 2D in a region which is infinite in x, semi-infinite in y, and bounded by a function of x (h[x] in my code) close to y=0....
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### How to plot solution of first order time dependent differential equations with other parameter not with time

I am trying to plot the solution given in the code with respect to "delc", not w.r.t time "t". I don't know what to do for getting the plot between solution and value "delc" which vary 0 to 2. The ...
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### Calculate sensitivities of differential algebraic equation

I would like to calculate sensitivities for a DAE. The DAE can be solved in Mathematica by: ...
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### AppendTo inside ParallelMap

I think this question has never been fully answered. In here the problem has already been mentioned, but let me give a MWE. I will solve a given ODE for a wide range of initial conditions and I want ...
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### The NDSolvevalue of MMA can not be used to solve the finite element problems according to the stress boundary conditions

The NDSolvevalue of MMA can well solve the finite element problems according to the displacement boundary conditions ...
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### A system of differential equations [closed]

Consider the following system of differential equations: $$x'(t) = a\, x(t) - b \,x(t) y(t),$$ and $$y'(t) = c\, x(t) y(t) - d \,y(t),$$ with $$x(0) = x_0, y(0) = y_0$$ For example, we may have: <...
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### Ground state Of Gross Pitaevskii Equation

I want to plot the ground state of Gross-Pitaevskii equation using NDSolve. I am using the following code: ...
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### NDSolve and Euler method

I would like to solve $y'(x)=x^2-y^2,y(0)=4$ with two ways, NDSolve and Euler method, and with Runge-Kutta maybe. Then, I 'll try to plot all of them in one graph. I had with NDSolve: ...
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### Why can't MMA solve this system of differential equations?

This system of differential equations can be solved in order to obtain the expression of x[t] y[t] z[t] ...
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### Maximizing Output from ParametricNDSolve [closed]

Given a system of differential equations that are dependent on two parameters, such as the system below (the equation below is not that important, I am interested in a general procedure given a ...
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### Unexpected stiff system error [closed]

Let there be the following functions ya[t_, x_] := Cosh[t*x] za[t_, x_] := Sinh[t*x] wa[t_, x_] := x*Sinh[t*x]^2 One can verify that the following PDE's hold <...
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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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