Questions tagged [differential-equations]

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

4,197 questions
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Solution to eigenvalue BVP using NDEigensystem to high precision

I'm trying to solve linear (non-self-adjoint) boundary-value problems to as high precision as possible (optimally 1e-15). For example, the below code solves for the first 5 eigenvalues of the harmonic ...
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Is there a way to find the analytical solution of the PDE containing mixed derivative?

In this equation $A$ and $B$ are constants. I want to find the analytical expression for this. Please let me know if it's possible to do this in Mathematica. Also, Are there any other conditions that ...
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Solving numerically an initial value problem on an unbounded domain

I wish to solve the pde: $$-\frac{1}{1-t}\partial_x^2\phi+t^4(1-t)\partial_t^2\phi-t^4\partial_t\phi=\mu^2 \phi,$$ with initial conditions $\phi(x,0)=\cos(\mu x)$ and $\dot{\phi}(x,0)=0$ for some time ...
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Eigen value solution of coupled ODEs

I want an eigen value solution of following coupled ODEs: But the code showing errors. ...
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Encountered non-numerical value for a derivative at t == 0 [closed]

I am exploring the Swinging Atwood Machine in my theoretical mechanics course. I have derived the following motions of equations and am trying to solve the ODEs with the specified parameters. My goal ...
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Hopf bifurcation for delay prey-predator system

I am trying to plot the Hopf bifurcation of delay system \begin{eqnarray} &&\displaystyle{\frac{dx(t)}{dt}=r\,x(t)\left(1-\frac{x(t)}{k}\right)-\frac{a\,x(t)\,y(t)}{(x(t)+A)}-E\,q\,x(t)},\\[0....
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NDSolve error: what does “It may help to rewrite the PDE in inactive form” mean?

I am trying to solve a set of partial differential equations numerically: ...
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Nonlinear Schrödinger equation

I have the code (taken from Mathematica):: ...
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Unable to get the expression of solution in DSolve

I am trying to solve the 1D Diffusion equation for a sigmoidal function. However I cannot the expression of the solution ...
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Verification of plotted points of intersection and curve orthogonality

A unit circle and tractrix (with differential equations respectively), $$\cos \phi =y;\, \sin \phi= y$$ and tangent slope $$\phi = \theta +\pi/2$$ are plotted to verify orthogonality. Due ...
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Solving and plotting an ODE in polar coordinates

I'm super new to Mathematica, but it's the software used at my school, and I'm really trying to get better at it. While I'm new to Mathematica, I'm not new to other STEM topics and am doing some ...
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NDSolve gives unexpected results when using the method of lines

I've been trying to solve the following PDE using the NDSolve function but it seems something is not working properly. The PDE is a the heat equation on polar coordinates and assuming angular simmetry:...
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Evaluating Hough functions by using NDEigensystem on the Laplace tidal equation

Currently I am looking into the use of Mathematica to solve the classical tidal equation of M. Laplace: $$\mathcal{F}\Theta+\gamma\Theta=0$$ whose eigenfunctions $\Theta$ are the Hough functions. ...
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Problem solving PDE with boundary conditions

I have the following PDE:  \frac{\partial }{\partial x}\left(G_x \left(\frac{\partial \phi (x,y)}{\partial x}-y\right)\right)+\frac{\partial }{\partial y}\left(G_y \left(\frac{\partial \phi (x,y)}{\...
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Errors in solving coupled pdes

I am trying to solve following coupled PDEs: I am not sure about suitable BCs. ...
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Using NDEigensystem to solve the Mathieu equation

To be able to apply the differential equation capabilities of Mathematica to my graduate thesis, I am trying to apply NDEigensystem to an eigenproblem whose solution I know, but I am having some ...
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Is this second order D.E. is solvable

DSolve[{(2.248*10^12) x^2 y''[x] + (4.496 x - 50.535)*10^12 y'[ x] - (1.17977*10^32) (x^3 Exp[-2 x] y[x] == 0, y == 10^-5.3}, y[x], x] You can use b.c. ...
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NDSolve ERROR: There are more dependent variables, than equations, so the system is underdetermined

I have a question concerning NDSolve and a system of differential equations. I have 4 variables and 4 equations. Why do I get this ERROR :There are more dependent variables, {f[j,p],U[j,p],(f^(0,1))[...
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NDSolve outcome depends on system size?

I tried to solve a simple wave equation numerically and plot the result within the time range t=0...1. Now when I change the tmax in the NDSolve the outcome of my plot (I don't change anything else ...
I am trying plot vector field of a dynamical system together with highlighting some area using some inequality constraints. My state-variable for vector fields are $x$ and $y$. The following are ...