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

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7
votes
2answers
345 views

Click in a vector plot to plot several solutions of a system of differential equations

I am aware of the Locator button and I am aware of the Equation Trekker package, but they are not what I want to use. Here is what I specifically want to know how to do, if possible. Consider the ...
0
votes
3answers
103 views

Delay difference equation

How can I correctly specify and solve a system of delay difference equations in mathematica similar to NDSolve with regard to delay differential equations? For example if I want to "see" the values ...
0
votes
2answers
95 views

Using parts of piecewise function

I define: f[x_] := Piecewise[{{5, 0 <= x < 10}, {g[x], 10 <= x < 15}, {h[x], x > 15}}] Then I try to solve ODE: ...
0
votes
1answer
92 views

solving PDE with periodic boundary conditions

I want to solve a 2D-PDE that has the form ...
3
votes
1answer
165 views

How to solve Laplace equation in 3D?

Basically I want to solve Laplace equation for truncated octahedron in a cube matrix. The boundary condition is Concentration u=200 at surface of truncated octahedron and u=15 at boundary of cube. I ...
6
votes
1answer
113 views

DSolve giving strange error messages solving a PDE

Consider this set of PDE $$\left( x^{2}+y^{2}\right) \dfrac {\partial u}{\partial x}+n x y\dfrac{\partial u}{\partial y}=0$$ have general solution $$u\left( x,y\right) =f\left( \dfrac {1}{n-1}\dfrac ...
0
votes
1answer
105 views

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 ...
0
votes
1answer
82 views

Phase Portrait Trajectories

How do I make a phase portrait which looks like the ones demonnstrated here? Not the fancy version where I can use the controls to change it, just a screen-shotted version of say a spiral point? Any ...
0
votes
0answers
56 views

Solving a system of differential equations using NDSolve

I am trying to model the descent of a diver jumping from space, and have the following system of equations: ...
-1
votes
1answer
75 views

Using InterpolatingFunction in equations

I tried to use InterpolatingFunction in another ODE, but it doesn't work, because it seems for Mathematica that 2 functions are unknown instead of one. ...
0
votes
0answers
34 views

DSolve of the system of two equations with known constants

In my previous post DSolve solution of two unknowns we conclude that Math 10 obtained results fast and that Math 9 did not give the solutions at all after one day. Now I have a problem if there are ...
2
votes
0answers
91 views

System of Partial differential equations

I am trying to solve numerically a system of 3 partial differential equations and I am facing a problem. My functions are f[x,t], ...
2
votes
5answers
189 views

Simplify an integral involving trigonometric functions

We were doing variation of parameters in differential equations tonight and had to do the following integral, the result given by hand calculations. $$\int \cos t\tan^2 t\,dt=\ln|\sec t+\tan t|-\sin ...
-2
votes
1answer
47 views

Find constants of differential equations [closed]

I have the equation $y'' + 16y' + 64y = 0$ Repeated root of aux eqn $r = -8$ Given the initial conditions, how do I solve for the constants $A$ and $B$? ...
0
votes
1answer
51 views

Solving coupled ODEs with NDSolve

Given the system of differential equations: $i\frac{d}{dt}c_{1}(t)=H_{12} E(t)e^{(iw_{12}t)}c_2(t)+H_{13} E(t)e^{(iw_{13}t)}c_3(t)$, $i\frac{d}{dt}c_{2}(t)=H_{21} E(t)e^{(iw_{21}t)}c_2(t)+H_{13} ...
7
votes
3answers
317 views

Envelope for harmonic oscillator [duplicate]

I am able to take the expression $\cos 11t-\cos 12t$ and use the sum to product identity to write it in the form $$\left(2\sin\frac t2\right)\sin\frac{23}{2}t.$$ I can then plot the function and use ...
2
votes
0answers
66 views

DSolve solution of two unknowns

I have one problem with the solution of the system of two differential equations. I waited hours, but Mathematica didn't give me a solution. Is there any way to obtain the results if we suppose that ...
3
votes
1answer
85 views

How to deal with the discontiuity in the solution of NDSolve?

I have a set of differential equations that describe the air temperature dynamics in a heated channel.The problem is that the solution becomes unstable and creates a discontinuity but physically it ...
2
votes
1answer
63 views

WhenEvent error in NDSolve

I’m trying to solve a discontinuous differential equation where there are lost of energy when the trajectory cross the discontinuous manifold. The code I used was ...
0
votes
0answers
36 views

NDSolveValue:dsvar error in a system of non linear differential equations generated using a Table

I have a system of 4 non-linear differential equation, that I generate using Table command. On solving, I keep getting a dsvar error that is not going away. I debugged my code and figured it has to do ...
1
vote
1answer
162 views

error DSolve::dsfun: cannot be used as a function

I tried to solve system of ODEs, but something was wrong. ...
5
votes
2answers
93 views

Initial time as parameter in ParametricNDSolve

I need a help with the function ParametricNDSolve. My goal is solve the equation \begin{array} &&\dot{x}(t) = y(t) \\ &\dot{y}(t) = x(t)-1-\varepsilon Cos(\omega t) \\ &x(t_0) = x_0\\ ...
0
votes
1answer
97 views

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

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

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 ...
2
votes
1answer
88 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
votes
0answers
40 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
vote
1answer
90 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 ...
0
votes
1answer
113 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 ...
2
votes
2answers
130 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
votes
1answer
55 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
votes
1answer
112 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
votes
1answer
77 views

amplitude-phase modulation equations solution

I am trying to solve the following equation ...
2
votes
2answers
150 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 ...
0
votes
1answer
87 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 ...
0
votes
0answers
89 views

NDSOlve - 1D wave equation with boundary

I am currently trying to solve the 1D wave equation with Mathematica: $$c^2\frac{\partial u}{\partial x^2}=\frac{\partial u}{\partial t^2}$$ I want to do so for a cantilever with a tip mass: One ...
0
votes
3answers
122 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 ...
1
vote
1answer
119 views

PDE solution does not satisfy Neumann boundary conditions using NDSolve

I am trying to solve the free particle Schrodinger equation in 1D (hbar =1, Energy = 1, mass = 1), But specifying conditions only on x==0: ...
-2
votes
1answer
72 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
vote
0answers
51 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
votes
0answers
54 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
votes
0answers
36 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 ...
0
votes
0answers
17 views

Why does the assignment of values to coefficients make a difference to the completion time of DSolve?

I hope to solve the following DAE equations using DSolve, (simplified example, may not be solvable): ...
0
votes
0answers
69 views

Divergence in the initial value problem solved by Ndsolve

here is to ODE I need to solve: ...
0
votes
0answers
85 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 ...
0
votes
0answers
38 views
0
votes
0answers
22 views

Solving an inhomogeneous partial differential equation [duplicate]

Here is my inhomogeneous partial differential equation: $$ \left ( \frac{\partial^2 }{\partial \rho^2}-\frac{1}{\rho} \frac{\partial }{\partial \rho} + \frac{\partial^2 }{\partial z^2}\right ) \psi= ...
1
vote
1answer
70 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 ...
1
vote
1answer
66 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 ...