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

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0answers
24 views

How to solve and plot this 2nd order non linear ODE?

Is this the correct way to plot the solution of this ODE from $(-8, 8)$? $$y'' - (1 - (y')^2)y' + y = 0$$ ...
0
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0answers
11 views

Fredholm Integral Equations

Please i'm having problem obtaining the solution of the.homogeneous Fredholm Integral Equation of the 2nd kind, with separable kernel.. I always get a zero if i use the normal method i was taught for ...
0
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0answers
34 views

Estimating inherent parameters for projectile under influence of wind in 3D based on measured data

The goal of this is to be able to estimate the drag constant $k$ and mass $m$ for a projectile based on measured landing coordinates $P$, start speed $v$ and launch angles $\varphi$ and $\theta$ ...
0
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0answers
63 views

How to solve a heat flow equation [on hold]

I am a beginner in Mathematica. I was wondering if anyone could give me some pointers as to how to solve following type of equations. During a particular time interval, ...
0
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1answer
32 views

NDSolve emitting error message NDSolve::ndnum [on hold]

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 ...
2
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1answer
35 views

How to write ODE to standard form?

Package like odepack needs the ODE written in standard form, which means write the high order ODE to first order ODE equations. The steps of converting ODE to ...
0
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0answers
29 views

Graphics Plotfield

A number of older books use the command: <<Graphics`PlotField` But Mathematica 10.0.2 says it cannot find it. Now, I know VectorPlot, but I am wondering if ...
1
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1answer
59 views

Failed to create a special random-disturbed initial condition for partial differential equation

I try to use BSplineFunction to creat a initial condition for NDSolve which has periodic boundary condition, that is realized by ...
-1
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0answers
63 views

Linearization of differential equations at first order

Currently, I migrate my Maple Code to Mathematica code. On a part linked to linearization, I meet some difficulties. In fact, i try to linearize some differential equations around an equilibrium ...
0
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1answer
94 views

Generate a small random disturbance on a flat surface for NDSlove

I want to generate a small random perturbation on a flat surface defined on a square domain, e.g. 1 + 0.05 rand(x,y), which can be used as initial condition with periodic boundary conditions in ...
1
vote
2answers
92 views

Linearization of differential equations

I was wondering if one could define an operator such that, when I give a certain number of (differential) equations as an output, and an "equilibrium" value for each of the variables, it returns the ...
0
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1answer
45 views

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 ...
0
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1answer
86 views

Solving Integro-Differential equations

I need help solving this equation. Is there a built in function that solves this type of equations? DSolve wouldn't work. Updated equation: ...
-1
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1answer
69 views

amplitude-phase modulation equations solution

I am trying to solve the following equation ...
2
votes
2answers
101 views

How to change the form $A\cos \omega t + B\sin \omega t$ into the form $\sqrt{A^2+B^2}\cos(\omega t-\phi)$ [duplicate]

I'm preparing notes for teaching next week's class in differential equations. My hand calculation solution of $$y''+192y=0, y(0)=1/6, y'(0)=-1$$ is $$y=\frac16\cos 8\sqrt3 t-\frac{\sqrt3}{24}\sin ...
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votes
1answer
50 views

Use ParametricNDSolve with Plotting

I am attempting to solve a differential equation of the form $$ \frac{dx}{dt}=ax+by \\ \frac{dy}{dt}=cx $$ with parameters $0<a<1$ and $a,b,c \in \mathbb{R}$. I am able to use NDParametric ...
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votes
3answers
88 views

How to define a function

How can I define a function which depends on a function of x? Something like this f[u[x]_,u[x]']= u[x]' + a [x] u[x] +b[x] I think I wasn't enaugh clear. If I ...
0
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0answers
47 views

How could I solve following equation? [closed]

I am quiet new to Mathematica. I was wondering if someone could give me some pointers towards solving an equation of this sort: Here is what I know: The change of temperature, T (Celsius) with ...
-2
votes
1answer
59 views

Transform differential equation to get equilibrium position

I would like to determine the equation in the equilibrium position. eq = 1/2 g l m Cos[θ[t]] == J (θ^′′)[t] ...
1
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0answers
37 views

ParametricNDSolveValue over a region

I'm getting the following behavior I don't understand when using ParametricNDSolveValue over a region. You can reproduce the behavior considering Poisson's equation ...
0
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0answers
30 views

NDSolve — using a PDE solution in another PDE

My problem is to use the numerical solution of a PDE as a function appearing in another PDE. Here is the code solving the first PDE (heat equation in a domain) : ...
0
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0answers
25 views

Multidimensional Fourier PDE solution and and exact solution are scaled by $(2 \pi)^{2}$

I'm solving a partial differential equation (Stokes equation) in a periodic domain in three dimensions with fourier transforms. I'm using Fourier[] mathematica routines to perform the discrete ...
-2
votes
0answers
25 views

Assigning values to constants after solving a set of differential equations [closed]

I solve the equations of 40 variables. Three of the equations are differential equations. Therefore, it is a set of differential algebraic equations. This is the following set of equations: ...
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0answers
55 views
0
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0answers
78 views

To find a surface with constant Gauss curvature

Please help me use NDSolve to find a surface with constant Gauss curvature $K$ in Cartesian coordinates. I have no previous experience with such differential ...
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0answers
37 views
1
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1answer
48 views

Particle motion with discrete values for the potential

Sorry if the question seems trivial, but I am new to physical simulations in Mathematica. I have a numerical estimation of an electric potential $V(x)$ in 3D, to be more precise I have a matrix ...
0
votes
1answer
36 views

NDSolve`Reinitialize start from previous solution but with different boundary conditions

I am solving a set of coupled partial differential equations (some variation of a 1 dimensional compressible fluid flow). I want to solve the equations (NDSolve, this works fine) but then continue ...
1
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1answer
92 views

Help with plotting and improving code

I'm trying to solve a coupled DDE. Here is my code ...
0
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0answers
35 views

Linear system of stochastic differential equations

I want to solve linear system of differential equations of the following form $$X'[t] = M.X[t] + R.X[t]*\lambda[t]$$ where $X[t]$ is a vector of coefficients I want to have at time $t$, $M,R$ are ...
0
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1answer
59 views
0
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1answer
60 views

Differential equations DSolve constant issue

After using DSolve to a set of differential equations, three constants arise. They are C[1], C[2] and C[21]. I have checked thoroughly that there are no C[3], C[4],....C[20]. It is quite mysterious to ...
1
vote
1answer
58 views

How to impose normalization condition (not initial condition) on DSolve or NDSolve?

I have a set of differential equations (or DAEs): $\begin{cases} 5x_{2} + 3x_{4} + 3x_{5} = \frac{dx_{1}}{dt}\\ 5x_{1} + 5x_{2} + 5x_{3} + 3x_{4} + x_{5}= 0\\ 3x_{2} + 3x_{4} + 10x_{5} = ...
3
votes
2answers
64 views

Problem with ParametricNDSolve

i have a strange problem with ParametricNDSolve. Given the sistem of differential euqations ...
0
votes
1answer
32 views

Numerical error in DSolve [duplicate]

I'm solving the 1D Poisson equation and am getting some funky numerical artifacts in the solution. ...
0
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1answer
72 views

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 ...
1
vote
1answer
69 views

System of differential equation with delay

I try to solve this differential system with delay: ...
0
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0answers
33 views

System of ODEs with Parameters

FYI: I am new to Mathematica so my questions are probably pretty amateur. I am attempting to write a code to numerically solve the system of equations: {dp/dt= ap-bpx {dx/dt= spx-yx where t is the ...
0
votes
0answers
63 views

Implicit/Backward Euler method

I'm trying to solve (and plot) a differential equation using Explicit Euler method and Implicit Euler method. The Implicit method worked out jst fine but I have problems with Implicit one... I made ...
2
votes
5answers
215 views

Taylor series without expanding factorial in denominator

A Taylor series is produced with the following code: ...
0
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0answers
40 views

Problem of WhenEvent in using variable updated in Event

equation1: value[inside RotationTransform] is a constant ...
1
vote
1answer
62 views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by ...
3
votes
1answer
102 views

What boundary is added when NDSolve::bcart pops up?

When insufficient boundary conditions are given to NDSolve for solving PDE, the warning NDSolve::bcart pops up: ...
0
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1answer
43 views

What function is the best for solving differential equations? [closed]

dy/dt = -y^2, what is the best function to solve this equation?
3
votes
1answer
71 views

NDSolve grid refinement for PDEs

I am experiencing trouble when trying to solve a PDE for various parameter values within mathematica: The PDE in principle can easily be solved numerically, however the stepsize of the spatial ...
1
vote
1answer
83 views

Integral Curve Question using Contour Plot

The ODE $$(xy-2)+(x^2-xy)y'=0$$ is NOT an exact differential equation. However, if I multiply both sides by an integrating factor $\mu=1/x$, the resulting equation ...
1
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2answers
41 views

Filling a region defined by a reduce command

I'd like to shade the region defined in the xy-plane produced by this code: ...
0
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0answers
86 views

Simulate a polygon bouncing with collision detection inside a circle/polygon

Simulate a polygon bouncing with collision detection inside a circle/polygon. the example can be see in help page by searching WhenEvent; ...