# Questions tagged [differential-equations]

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

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233 views

### How to speed up the integral in NDSolve?

On the MMA.SE, there have been several question on how to solve equations including integral using NDSolve, see example 1, example 2, and example 3. Many people, ...
216 views

### DEigenvalues and NDEigenvalues return different values

In the following example, DEigenvalues and NDEigenvalues return different results despite having identical arguments. Does anyone know why? (I use Mathematica 11.3) ...
75 views

### Does 2D time dependent Schrödinger equation example work?

I have entered the example: www.wolfram.com/mathematica/new-in-10/pdes-and-finite-elements/solve-a-wave-equation-in-2d.html into 12.0, and gotten an error message in the uifWave assignment. It says,...
52 views

### Evaluation functions with lower and upper limit ODE?

How do I find the numerical value of y at 0 and also at 1. Here is my code. I appreciate any help. ...
33 views

### Implicit definition of a coordinate in differential equation [duplicate]

I would like to solve the following differential equation $\frac{d^2 \psi(r_*)}{dr^2_*} + (\omega^2 - V(r)) \psi(r_*)=0$ and the boundary conditions are $\psi(\inf) = \psi(-inf) = 0$. The problem is ...
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### How to integrate this expression one time? [duplicate]

How can I integrate this expression? I want to have the second derivative of V i.e. V''[r]. Note that, you can multiply it be ...
179 views

### How to solve this differential equation analytically?

How can I DSolve the following differential equation? Is there an analytical answer to this equation? ...
44 views

### Problems with DAE solution: “Structural analysis indicates that 1 initial conditions are needed to fix the state of the system…”

I'm trying to solve the following problem: ...
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### Problem with using NDSolve on wave PDE on string

I am trying to verify my hand solution for wave PDE in 1D, on a string. The solution I get from NDSolve does not match the analytical solution. This is a string, ...
58 views

### DSolve does not solve 2nd order linear PDE with variable coefficients

I find that DSolve can solve DSolve[x*D[u[x, y], {x, 2}] - D[u[x, y], x, y] == 0, u, {x, y}] or ...
44 views

### Solving a System of Differential Equations for Pendant Drop Application

So I'm trying to solve the system of differential equations describing a pendant drop. The system is as follows: ...
31 views

### Plotting 2D and 3D data for a nonlinear system in mathematica

I had to plot various nonlinear differential equations. But because of a large number of equations for large spans of time and other considerations, the program has become too heavy to be run on my ...
164 views

### Workaround for DSolve in V 12 when it gives undefined as solution to 1D heat PDE?

Reported to WRI CASE: 4278450 Comparing the following, all done from clean kernel The strange thing is that V 12 can solve this same PDE without the assumptions ...
71 views

### How to solve a differential equation like this one? [closed]

Does anyone know how to solve this equation in Mathematica dx/dt = f(x) + u where f(x) = -x, if x < 1 or x = 1
105 views

### WhenEvent&NDSolve: How to detect saddle point?

I'm considering a simple ode. With the help of WhenEvent and Discrete Variable it is possible to detect the sign of the ...
55 views

### Numerical solution of a PDE having boundary conditions

I am solving a PDE using Mathematica. and I would like to know how to implement the condition that the three-variable function u[t, x, z] ...
135 views

### How to fit polynomial curve using Mathematica for multiple inputs?

I am new to mathematica. I have 3 inputs and 1 output. I want to find the 'N' th degree of polynomial which would approimately fit my dataset. I tried FindFit but it does not solve my problem. I also ...
49 views

### DSolve Coupled Equations

I'm new to Mathematica, and I am trying to solve a system of coupled equations with complex conjugates using DSolve before trying NDSolve. So far my code does not work, I was wondering if maybe you ...
49 views

### How to solve a complex equation

I am trying to solve a complex equation for 'z' in terms of 'f'. At the moment my Mathematica is stuck running... Just wondering if anyone has any ideas, I know 0 < z < 40 if that helps. <...
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### Some issues with DEingesystem

I would like to solve (get its eigenvalues/vectors) the Sturm-Liouville problem, for the following differential operator: $L =\partial_{r} \partial_{r} \psi(r)$. Also, I would like to impose the ...
64 views

### Piecewise with differential equations

I have the following differential system. The calibration I use is as follows ...
66 views

### How could I know the Method adopted in NDSolve?

In NDSolve, different methods may lead to different results. For my codes ...
135 views

### Runtime too long for NDSolveValue, FindRoot breaks down at sharp turns

I have two equations:  \frac{2}{3}\thinspace\left(\frac{\varepsilon}{\Delta}\right)^{\frac{3}{2}}=\sum_{i=1,2} \sigma_i\lambda_{i}\left(1+\lambda_{i}^{2}\right)^{\frac{1}{4}}E\left(\frac{\pi}{2},k_{...
153 views

### Problem with boundary condition 2D heat transfer

I want solve this 2D Heat transfer: So at Mathematica: ...
33 views

### How should I enter systems of equations as index notation?

I'm trying to numerically solve a system of ODEs that I've worked out in index notation where it's not clear to me what the matrix representation of many terms would be, and writing each scalar ...
77 views

### DSolve of second order DE results in InverseFunction

As a result of evaluating DSolve[a''[t] a[t] - (1 - C) a'[t]^2 + (Cc - C L/3) a[t]^2 + (C - 1) k/2 == 0, a[t], t] I got an ...
266 views

### Find multiple solutions of a nonlinear ODE

I have a nonlinear ordinary differential equation with two parameters c and R in the form of: ...
67 views

### Piecewise function not evaluating in NDSolve

Perhaps it's something obvious, but why does this simple piecewise function (as well as other conditionals) not evaluate in NDSolve: ...
78 views

### Getting the coefficients of a series that solves a differential equations

I have an example from Stewart's Calculus where the equation $y'' + y = 0$ is solved using power series. The equation ...
74 views

### Getting errors from ParametricNDSolveValue

I am a newcomer to Mathematica (use ver 9.0). I just want to fit the experimental data to a system of odes' by using NonlinearModelFit. The data, contains time in the first column and product ...
19 views