# Questions tagged [differential-equations]

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

3,826 questions
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### 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" ...
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### 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 ...
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### 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: ...
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### 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: ...
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### 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 ...
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### 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. ...
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### 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 ...
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### DifferentialRoot with parameters that “are not exact numbers”

In the course of developing an answer to 185859, I encountered the following difficulty. With ...
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### 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). ...
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### 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: ...
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### 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/...
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### 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. ...
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### 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: ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Cartesian to Polar Transformation Bug?

I was trying to do this problem with Mathematica Equating Coefficients of Cos and Sin We have ...
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### 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 ...
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### 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 ...
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### 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: ...
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### DSolve can not solve my PDE

I'm having some trouble using Dsolve to solve a partial differential equation. This is my code: ...
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### 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), ...
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### 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 ...
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### 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: ...
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### 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 ...
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### 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 ...
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### 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] ...
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### 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: ...
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### 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. ...