Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
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How to solve the following GR PDE?
Someone could help me for solving the following GR PDE? (this code do not work yet)
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7
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How to select coefficient of an exponential function
Suppose I have these set of equations:
sol = DSolve[{
x'[t] == -RandomReal[]*x[t] + y[t],
y'[t] == x[t] - *y[t] ,
x[0] == 1, y[0] == 0}, {x[t], y[t]}, t]
The ...
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Compute StateResponse for list of inputs
How do I find the state response of a system for a list of inputs? Simply writing an array in the place where the input enters as an argument of StateResponse ...
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Solving ODE system with NDSolve: "singularity or stiff system suspected" [closed]
I'm trying to solve a set of 4 ODEs as specified below, however I'm getting this error
...
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Mathematica 10.3 Dsolve solving a simple PDE [closed]
I tried to use Mathematica 10.2 and 10.3 to solve this simple PDE and I want to a general solution. But it seems not working.
DSolve has been improved in v10.3. But we see it's perhaps not improved ...
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NDSolve breaking down
I'm trying to model a situation involving charged sphere in a dynamic electric potential, and find out how the rotational motion of the sphere affects the translational dynamics in two dimensions. ...
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Can I tell DSolve to solve a first-order ODE by method of separation of variables?
I meet a first-order ODE
$$\frac{dy}{dt}=\frac{a(\ln\frac{1-c}{1-y})^3}{\frac{b-y}{1-y}+\ln\frac{1-c}{1-y}},$$
where $a,b,c$ are constants. The ODE is subjected to the initial condition $y(t=0)=y_0$.
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NDSolve::ndode: Input is not an ordinary differential equation [closed]
I am new to Mathematica. I am working on solving the following different equations numerically written in the code as below.
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Checking the solution of a differential equation with a boundary condition depending on an arbitrary function
I have the partial differential equation:
$\qquad U_{x} - 4 x^{2} U_{t} = x U, \qquad U(x,0)=f(x), \qquad x \in (- \infty, \infty), \qquad t \in (0, \infty)$
Where $U_{x} = \frac{\partial U}{\...
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The length of the derivative operator Derivative[0,0,2,0] in \ f^(0,0,2,0)[x,y,z,t] is not the same as the number of arguments. >>
I'm trying to solve Maxwell's wave equation but am faced with an error message
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Problem in the solution of the simultaneous Ordinary Differential Equation [closed]
When i am running the following command
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Solving an NODE in series
How can I solve this NODE in series
y''[x]^2 + (1/2)*y'[x] + (1/2) y[x] == p x + q.
`p` and `q` are constant.
But do not know how to actually solve it with ...
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How to solve constraint differential equations using If function
I have to solve a series of differential equations along with a constraint that has to be satisfied at each point of time where $t\in [0, 100]$
The model parameters are
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ParametricPlot not plotting the results I'm getting from NDSolve
I try to plot a phase diagram with ParametricPlot but everytime Mathematica does nothing.
I start by ;
...
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2
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Matrixform ndsolve for mobile robot dynamic equations
Error is:
NDSolve::ndsdtc: The time constraint of 1.` seconds was exceeded
trying to solve for derivatives, so the system will be treated as a
system of differential-algebraic equations. You ...
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second order nonlinear ode
I need to solve the following equation for $u_n(t)$:
$u''=\frac{u'^2}{2u}+\frac{3u^3}{2}+4tu^2+2\left(t^2+\frac{n}{2}+(2p+1)\frac{1+3(-1)^n}{4}\right)u-\frac{n+(2p+1)(1-(-1)^n)}{4u}$
where $p$ is a ...
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2
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Problem with NDSolve: derivative interpreted as square [duplicate]
I am using Mathematica 9, and trying to solve a very easy differential equation with NDSolve. The code I have is
s=NDSolve[{y'[x]==y[x],y[0]==1},y,{x,0,1}]
but I ...
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Solving differential equation (Analytical or Numerical)
I want to solve the following differential equation for $0 < x < 1$
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102
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NDSolve Problems with Cardiovascular Modeling [duplicate]
I am trying to use 27 simultaneous differential equations to model the cardiovascular system. I have the following code, however, the output isn't giving interpolating functions, but rather another ...
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Solving differential equation with Variable constans?
How do I solve the following differential equations using Mathematica under the assumptions:
If Abs[r[t]]<50 ->A=0.5;B=2;
AND
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How to write absolute value and square root in one equation?(runge kutta) [closed]
I got some problem when I run my program. It hangs when I run it.
This is my coding for runge kutta Geometric mean(RKGM).
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166
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NDSolve::bcsol?
I'm writing a code to numerically solve a differential equation. It has to repeat the process several times since there is a variable involved which is unknown, and the equation is fit to some ...
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Forcing solutions to avoid Root[]
I'm solving a system of ordinary non-homogeneous differential equations (4 equations). The solutions will include some algebraic equations solutions as known from text books due to the use of an eigen ...
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Implicit differentiation and the Folium of Descartes [duplicate]
Given the function (Folium of Descartes) $x^3 + y^3 = 3xy$, how would I find the equations for tangent and normal lines at the point $\left( \frac{3}{2},\frac{3}{2} \right)$?
I know that I must use ...
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706
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NDSolve emitting error message NDSolve::ndnum [closed]
I am trying to solve this system
equn1 = ψ'[x] == - Elec[x]
equn2 = Elec'[x] == - ((di/ a)^2)[(Exp[ψ[x]] - (x/(xoi*Sqrt[-ψ[x]])))]
For that I am using ...
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Unable to break out of two Do loops
I wrote a mathematica program to solve one dimensional schrodinger equation for particle in box model with zero potential. I used two do loops to achieve the task. The inner do loop will solve ...
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192
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Method that combine LinearSolve and Dsolve for a set of differential equations?
I have a matrix for example:
$\begin{bmatrix} 0 & 5 & 0 & 3 & 3\\ 5 & 5 & 5 & 3 & 1\\ 0 & 3 & 0 & 3 & 10\\ 1 & 3 & 2 & 3 & 10 \\ 1 &...
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Tough Calculation, novice mathematica user
I have an equation, that I've been calling $b_N(x)$ that satisfies the following identity:
$$-Nb_N(x)^2=(x-N)b_N(x)+xb_N'(x)$$
where $b_N'(x)$ is the first derivative. I take the derivative then of ...
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Plotting a solution of DSolve
I am trying to plot a solution of a differential equation system. This is what I have:
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Plot slope field in Mathematica for a difficult differential equation
I am trying to plot slope field for $\ddot{a}(t)$ for this differential equation but I don't know how to
$\frac{d}{dt}\ddot{a}(t)=2\frac{\dot{a}(t)}{a(t)}\ddot{a}(t)$
I want to show that already ...
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Parallel computation of NDSolve and a problem
I used this code to solve a system of differential equations:
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Solving systems of equations and derivatives
I am new to Mathematica, and I'm not sure how to solve a system of equations that include differentiation.
Given that f and g are differentiable functions:
...
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NDSolve in exact points - nonlinear equation (Degrees and Radians confusion)
I found solutions of two nonlinear equations, but I have three small questions.
First I am in confusion because of initial value. The system is mechanical and unknown ϕ is an angle, which I set to ...
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Plotting the discrete solution to a PDE
So I went through all the grunt work of solving a PDE in discrete form for a research project. Now I have a Temperature solution as a function of time and space:
$$
T_{i}^{n+1}=\left( \dfrac {\...
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Setting plot size within vector; dynamic slider (two part question)
I have a question about the size of a plot in mathematica. I'm working on some differential equations (a simplified model of heat transfer in a building). I've programmed it so that you can set ...
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1
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530
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Infinite expression 1/0.^(1/4) encountered in NDSolve
I am trying to solve very simple system of coupled differential equations using the NDSolve function, but I am getting ...
- 195
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663
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Cannot get specific value from NDSolve (multiple functions)
I am trying to solve six connected differential equations. This is my code:
...
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Problem evaluating results of DSolve (Power::infy)
So, after browsing through older posts to see if anybody else could have had the same problem, I have come to the conclusion that I am stuck. That bothers me, especially because it should be straight ...
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How to combine DSolve and FindRoot
As my differential function is relatively complex I do not want to do the detour of finding an explicit solution via DSolve for it but rather use an FindRoot-like approach by guessing initial starting ...
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Manipulating and using result of DSolve
I have an unsightly looking equation that nonetheless has an analytical solution. The solution is ugly as hell, but exists; I use the following code with the DSolve ...
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Bifurcation diagrams for system of equations
I am interested in constructing a bifurcation diagram for parameter a in the dynamical system given in the code below. I want to see how parameter changes affect the stability of the system. The ...
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DAE - varying initial conditions
I want to solve a DAE-system and I want to vary more than one initial conditions and to manipulate them. I looked here:
Putting NDSolve into ParametricPlot
But it does not work:
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How can I suppress message "... cannot be used as function"?
I'd really appreciate your help. The code gives me a solution, but in the end it says it cannot be used as function, which is not true.
Script:
...
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Applying l'Hôpital's Rule to NDSolve with Piecewise Function
OK, so I've been working on this problem for over a week and it's driving me crazy.
I'm trying to solve a system of two differential equations in $x(t)$ and $y(t)$ using a "time-elimination method," ...
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DSolve output - understanding how to extract result
I'm a little confused with how to use the output from DSolve. The following works
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Understanding the example of sensitivity analysis in Documentation using ParametricNDSolve
There is an example in Documentation for studying sensitivity analysis, using ParametricNDSolve:
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