# Questions tagged [differential-equations]

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

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### Analytical solution of second order linear differential equation with boundary at infinity

I am a new user to Mathematica and I would like to solve a simple second-order differential equation as follow: $y''[x]+\frac{(D-1)}{x}\times y'[x]=k\times y[x]$, where $D$ and $k$ are just two ...
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### Showing that a Hopf bifurcation exists?

I have the following system of ODEs: dx/dt = a/(1 + z) - Q*z dy/dt = Qx - qy dz/dt = qy - cz/(K + z). Assuming K = 1, Q = q < c, and a = c*(Sqrt[c/Q] - 1), is there a way to use Mathematica to test ...
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### Incorrect results of DSolve

Finding a fundamental solution of a certain linear partial differential operator, I try ...
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### Plotting a phase plane portrait of an oscillatory system?

I am trying to plot a phase plane portrait of the following system: dQ/dt = v*(z - Q)*(w^2 + Q^2)/(1 + Q^2) - Q dz/dt = k - Q where v = 1, k = 0.2, and w = 0.05. So far, I have the following: ...
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### NdSolveValue Freeze sensitive to initial condition

I am trying to solve the following system of non-linear differential equations: ...
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### Loops for every time step on a time-dependent function coming from NDSolve

I have a time-dependent function a[t], which comes from solving various differential equations. Therefore, to obtain the different values of ...
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### Why is Mathematica unable to solve this integral equation?

How to solve the following integral equation in Mathematica? eqn = y[x, z] == z + x*Integrate[y[t, v], {t, 0, 1}, {v, 0, 1}] sol = DSolveValue[eqn, y[x, z], {x, z}] ...
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### How to solve ODEs using deep learning in Mathematica [closed]

I have a number of ODEs (58) with 16 parameters and 9 variables. I want to solve the ODEs to obtain the analytical relationship between the parameters and variables. It is obviously that the ODEs ...
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### How to solve this set of integrated PDEs

Could anyone help me solve set of pdes with embedded integration? The pdes below is solvable , but can not be solved when I tried different parameters such as ...
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### NDSolver cannot give precise result for extremely small values

I would like to solve an ODE with MMA. The equation is simply the Coulomb law. However, I cannot get a satisfying result: ...
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### Any Mathematica techniques to calculate time takes to reach the equilibrium of a PDE solution

I am solving this PDE numerically (dimensions: spatial variable x and time t). I know how to solve my problem numerically (for a given range of time). The solution reaches its equilibrium after a ...
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### Stiff system problems with NDSolve

I'm trying to solve the two order differential equations using NDSolve. Here is the code: ...
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### How to plot poincare map as shown in below image for Duffing equation?

I am trying to plot phase diagram and poincare map. But I cannot get the poincare map as shown in the image below Phase Space ...
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### Solving Fokker Planck Equation with NDSolve

I am trying to solve the FPE for the steady state solution as in the paper (see equation 4, with G(s,m) as in methods): https://home.gwu.edu/~glan/files/2012.Nature.Physics%20-%20The%20energy%A8Cspeed%...
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### How can I Plot Phase Portraits Using ParametricNDSolve function(already know about StreamPlot function)?

I have a 2nd order ODE: $$\ddot{\phi}+3\dot{\phi}\sqrt{(\frac{8\pi G}{3})(\frac{1}{2}[\dot{\phi}^{2}+m^{2}\phi^{2}])}+\phi m^{2}=0.$$ I can use the StreamPlot command by breaking the ODE into a set of ...
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### I have a problem evaluating an ODE in Mathematica, where the error asks me to define a dependent variable?

I am trying to solve a series of linked ODEs in Mathematica (where the system describes the trajectory of a ball through the air). ...
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### Assigning A Symbol To A Second DSolve Solution

I am looking for a way to compress a lengthy DSolve solution to a single symbol, kind of like assigning a variable. I have this expression: ...
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### Supplying a seed for an iterative method in LinearSolve

Just a quick question. Does anyone know if it is possible to supply a seed for the iterative methods in LinearSolve? I have a large sparse system, and even using some Krylov iterative solver, my ...
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### Matrix differential equation with DSolve doesn't work

I'm trying to solve matrix differential equation with DSolve, but I got an error. ...
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### Can mathematica numerically solve this system of coupled integro differential equations?

Here's my system: R(x,y,t) is the concentration of a chemical that's diffusing across the box. The disk is a mobile sink for the chemical, which absorbs it in proportion to its concentration. The ...
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### FEM 1D 3D region coupling - speed up coupling using boundary integration

I am working on a simulation of the heat equation involving a 3D solid simulation coupled to a 1D fluid simulation (convective term of heat equation). I am using the method of false transient as ...
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### How to calculate precise higher derivatives of ParametricNDSolve solution

Higher Derivatives of NDSolve don't match the results from DSolve solution, can I somehow increase the accuracy of numerical method to match arbitrarily high derivatives? Equation I am using ...
I'm trying to solve a set of PDEs and am running into problems. The system is defined by: As can be seen, there are two dynamical equations for $\rho$ and $\phi$, but the equation for $v$ has no time ...