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Questions tagged [differential-equations]

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

2
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1answer
87 views

Plot of differential equations?

y=C/(x+1) ( I get it from sol=DSolve[y'[x]==-y[x]/(x+1),y[x],x]) How I can plot this "sol" ...
0
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0answers
60 views

Application of ODE

I got to do some assignment for my Student Research. 1. Cat and mouse are in room which is shape in sqare . Cat is in one topic square, mouse in another one. In topic square oposite than cat position ...
0
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2answers
65 views

Integrals of a Fourth order differential equation: Part A

Is it possible for us to get the value for integrals of a Fourth order differential equation in MMA. I attach the code that i have used in MMA: ...
0
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0answers
59 views

Solving wave equation on a disk with DSolve in cylindrical coordinates

I want to obtain the general answer to the wave equation: $$ u_{mn}(r, \theta, t) = [A\cos(c l_{mn} t) + B\sin(c l_{mn} t)]\ \mathrm J_m(l_{mn} r)\ [C\cos(m \theta) + D\sin(m \theta)] $$ where $ \...
1
vote
1answer
75 views

Second-order nonlinear boundary value problem

I am trying to follow this work, in which Eq. (11), the 2nd-order, nonlinear differential equation depends on a pair of parameters $ (\kappa, h) $. But now I only care about the case with a vanishing $...
5
votes
1answer
115 views

Help with 3D FEM calculation of a heat equation

I want to solve a heat transport problem in a long tube where 4 coolings rods are inserted. Fluid flows down axially, and there's radial heat conduction. First, the shape is defined: ...
1
vote
3answers
66 views

NDSolve output as input to another NDSolve

I want NDSolve to solve the problem $$y'(x)=0, y(0)=1, x\in[0,1] $$ and then use $y(x)$ to solve $$z'(x)=y(x), z(0)=0, x\in[0,1] $$. This is a toy model of the real problem. In the real problem ...
0
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0answers
54 views

Function for Domain of Differential Equatiion

Domain of d.e y'=f(x,y) is Domain[f] Union Domain[1/f]. I want to make function in Mathematica which will give Domain of any d.e and plot it. ...
1
vote
1answer
71 views

Double physical pendulum with constraint

I am working on double physical pendulum with fixed freedom of one bar. Angle te2 (angle of lower bar) can not be bigger than angle te1 (angle of upper bar) How I can make WhenEvent to get that? Thank ...
2
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1answer
53 views

DifferentialRoot with parameters that “are not exact numbers”

In the course of developing an answer to 185859, I encountered the following difficulty. With ...
0
votes
1answer
44 views

Solve nonlinear differential equation system (Plot solution)

When I solve the system of differential equations I get two solutions for each variable (See the picture). My question is how I can neglect one of the solutions at the plot (The yellow and the blue). ...
3
votes
1answer
60 views

Ideal transformer model (2 ODEs) warning “NDSolve will try solving the system as differential-algebraic equations”

I have a simple electrical circuit of an ideal transformer: I model it in Mathematica 11.3 with the idea to solve for secondary current and potential difference. Here is my code: ...
8
votes
0answers
210 views

From where to learn finite element method?

Can anyone reccomend me a book or site for learning finite element method with mathematica, besides wolfram language official site, https://reference.wolfram.com/language/FEMDocumentation/tutorial/...
1
vote
1answer
48 views

Combining ListLinePlot graphics with Show

I'm new to Mathematica working on a project for school. I'm trying to show the deflection of a cord over time by breaking it up into 14 points and plotting the x,y coordinates of each point over time. ...
0
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0answers
25 views

Problems using NDSolveValue to solve system of PDEs over 3D region

I am trying to solve a system of partial differential equations over a cube region. The text is as follows: ...
0
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0answers
67 views

Solving ODE with NDSolve with initial condition at -Infinity

I have just started using Mathematica. I want to solve a differential equation numerically with NDSolve. I have to specify an "initial condition" at ...
0
votes
1answer
55 views

NDSolve initial value not explicitly specified

I'm trying to solve for 2 first order coupled ODEs. I've got two initial conditions, and I can't get a solution. I've double checked my equation input and my initial conditions, and my NDSolve ...
1
vote
1answer
49 views

Plotting a nonlinear damped pendulum with adjustable damping variable

I am trying to graph the formula of the angle of a damped pendulum over time which starts at an angle pi/3 with 0 angular velocity. The angles used are too large to make use of the small angle ...
3
votes
2answers
120 views

NDSolve with boundary conditions at infinity

I have a feeling that similar questions have been asked before, but here goes. I'm trying to solve an ODE using NDSolve, with boundary conditions for one of the ...
0
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0answers
48 views

Cartesian to Polar Transformation Bug?

I was trying to do this problem with Mathematica Equating Coefficients of Cos and Sin We have ...
0
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0answers
44 views

Computing quadratic differential trajectories with Mathematica

There was a question about a particular case of this, Quadratic differentials; seemingly it contained too little information, so let me try again. This will be also a second take on my previous ...
0
votes
2answers
49 views

How can I plot the solutions to this overdetermined system of non linear ODEs?

I want to plot the solutions to: $$(l')^2 + (h')^2 = 1$$ $$(c-1)\sin(2l)=2l''$$ where $c$ is a constant, but I haven't been able to (I tried using NDSolve but didn't manage to do it). Can someone ...
0
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0answers
35 views

NDSolveValue seems to ignore a boundary condition

I am trying to solve a system of PDEs over a cilyndrical region. The text goes as follows: ...
0
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2answers
131 views

DSolve can not solve my PDE

I'm having some trouble using Dsolve to solve a partial differential equation. This is my code: ...
0
votes
1answer
41 views

Problem converting double integral to PDE and solving with NDSolve

I'm trying to use the well-known "trick" of converting an integral to a differential equation, which can be much faster if the integral has to be evaluated repeatedly (in my case millions of times), ...
0
votes
2answers
84 views

differential equation - evaluate and parametric plot [closed]

I have to solve the equation in range from 0 to 7pi: x''[t]-(1/2)(1-x[t]^2)x'[t]+x[t]=0 with boundary conditions ...
2
votes
1answer
53 views

Difference between FourierTransform and LaplaceTransform [duplicate]

There is an equation for example: eqn=D[c[x, t], t] == d D[c[x, t], x, x]; When I make a LaplaceTransform of it: ...
0
votes
1answer
87 views

Numerical solution of differential equation with boundary condition at infinity

I have the following ODE for a function $F(x)$: $F''-\frac{1}{x}F'-aF=0$ with the following boundary conditions: $F(x\to0) = 1$, $F(x\to\infty)=0$. It can be solved analytically: $F = \sqrt{a}xK_1(\...
0
votes
1answer
44 views

Can i plot different parameter differential equation phase plane in a line?

In order to compare with different parameter,can i use StreamPlot plot them in a line, for example: $$\dot{x} = Ax$$ When $A = [-1,0;0,-2]$, i can use code as ...
3
votes
2answers
51 views

Problems using DensityPlot when solving Laplace's equation

I am trying to solve Laplace's equation in 2 dimensions with potencial boundary conditions at the edges of an external square and an internal circle. Everything seems to work fine until the point ...
8
votes
1answer
139 views

NDSolveValue -difference between Version 11.2 and Version 11.3

I am trying to learn something about simulation of heat transfer by looking at this problem which is an answer by user21. If I try this in Version 11.3 the following happens: ...
1
vote
1answer
49 views

Taking the limit of a parametric function produced by ParametricNDSolveValue

I'm working on a project for hard-sphere scattering, and to solve the for the phase function $\overline{\delta}_l(k,r)$ I use the variable phase equation $$ \frac{d\overline{\delta}_l(r,k)}{dr} = -\...
0
votes
1answer
83 views

How can I solve this BVP using mathematica?

I need to solve the following BVP: $$(g^{-1/3}f'')'+ff''=0$$ $$(g^{-1/3}g')'+0.71fg'=-1.43775g^{-1/3}(f'')^2$$ With the following constraints: $$f[0]=0,f'[0]=0,f'[20]=1,g[0]=0.944175,g[20]=1$$ I used ...
0
votes
1answer
56 views

NDSolve and DSolve [duplicate]

So basically I have a system of linear equations for springs im trying to solve. stiffSpr is nonlinear and linSpr is linear. But it keeps telling me that its expecting an equation and not true. I can'...
1
vote
1answer
64 views

Defining the boundary conditions of a PDE

I'm first time use Mathematica and here is my trying of solving equation ...
1
vote
2answers
83 views
3
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2answers
202 views

Why does NDSolve blow up when given my ODE but bvp4c in Matlab does not?

I am numerically solving the following ODE initially using NDSolve in Mathematica(updated and corrected): $-(-\frac{z'(r)}{r \sqrt{z'(r)^2+1}}-\frac{z''(r)}{\left(z'(r)^2+1\right)^{3/2}})=A_1(z(r)+H)...
4
votes
1answer
86 views

Solving a stochastic dynamical system

I'm attempting to add gaussian white noise into a single equation of a 2 state variable dynamical system $$\frac{dx(t)}{dt}=1-x(t)\left(1+e^{-y(t)}\right)$$ $$\frac{dy(t)}{dt}=1-y(t)\left(1+e^{\frac{x(...
1
vote
0answers
26 views

Converting a second order PDE from one coordinate system into another [closed]

I am interested in converting a second order differential equation in partial derivatives from one coordinate system into another. To be specific from cylindrical coordinates to oblate spheroidal ...
1
vote
2answers
64 views

Solving non-linear PDEs

I wish to solve the equation $$\frac{dp(x,y,t)}{dt} = D\ \nabla^2 (p(x,y,t)) -C \ p(x,y,t) - R \ p(x,y,t)^2 $$ But, I get the error ...
0
votes
1answer
46 views

How can I compute the derivative of a variable after it is solved using NDSolve?

I have a 4th-order(with respect to x and 2nd-order with respect to t) pde which is solved easily using NDSolve for the variable v[x,t]. Now, I also want the value of 3rd-order partial derivative of v[...
1
vote
1answer
90 views

Computing the Lyuponov exponent for the Duffing system

Does anyone know (simple) Mathematica code for computing the Lyuponov exponent for the Duffing system? ...
1
vote
1answer
51 views

Mapping a boundary value problem: Jacobian in NDSolve and refining mesh close to a point

I would like to solve the (oversimplified!) BVP $u''(x)-u(x)=0,\qquad x\in[0,\infty)$ with the condition $u(0)=1$. I thought to remap this into the BVP problem $D[J^{-1}(\xi)u(\xi)]-J(\xi)u(\xi)=0, ...
0
votes
0answers
33 views

NDSolve dealing with message infinite expression and non numerical value non homogeneous differential equation

I'm trying to solve the following differential equation with some specific conditions ...
0
votes
0answers
41 views

Proper implementation of numerically integrated function inside a differential equation

I have a numerically-inverted function TP which is then fed to the differential equation below. My question is: What is the right way to implement this ...
1
vote
0answers
73 views

How can I plot the solutions of my ODE? [closed]

Consider the following code that solves an ODE. DJ[x_, y_] := (y[x] + x^2) y'[x] - x^2 y[x] == (y'[x])^2 DJ[x, y] ...
0
votes
0answers
67 views

How to solve Laplacian equation 3D in spherical?

Laplace’s equation is: $$ \nabla^2V=0 $$ The boundary conditions are: $$ V(r=0)=0 $$ $$ V(r\gg a)=-E_0 \cos\theta $$ My code is: ...
0
votes
1answer
75 views

Problem with solving differential equation using NDSolve

I am trying to solve differential equations subject to condition z[0] == 0 and z[tmax] == 10 Pi. ...
-1
votes
1answer
81 views

nlnum problem of NDSolve

I'm having a difficulty to NDSolve a ODE due to nlnum (according to the error message). Below is the code I have. First of all are functions: ...
1
vote
2answers
118 views

Getting error NDSolve::ndsz from my ODE

I'm trying to figure out why I am consistently getting singularity error when I'm trying to solve an ODE using NDSolve. Any help will be appreciated. ...