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

learn more… | top users | synonyms

0
votes
1answer
72 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 ...
-2
votes
0answers
39 views

How can I use the Euler's method to approximate $xy′ + y = e^2,\, y(1) = 2$? [duplicate]

I've been using the while syntax but it doesn't work.
0
votes
0answers
50 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: ...
0
votes
1answer
51 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
30 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
82 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], ...
1
vote
2answers
91 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
41 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
0answers
16 views

Differential equation : y'(x)=(x+y(x)+1)/(x-y(x)+2) [migrated]

I have a question related to the differential equations.I have to solve the following equation: y'(x)=(x+y(x)+1)/(x-y(x)+2) However I don't see what should I ...
0
votes
1answer
48 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
300 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
63 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 ...
1
vote
1answer
41 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
30 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
104 views

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

I tried to solve system of ODEs, but something was wrong. ...
5
votes
2answers
76 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
93 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
0answers
34 views

Fredholm integral equations [migrated]

I'm having problem obtaining the solution of the homogeneous Fredholm integral equation of the 2nd kind with a separable kernel. I always get a zero if I use the normal method I was taught for the non ...
0
votes
1answer
42 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
44 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
34 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
71 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
votes
0answers
81 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
votes
1answer
103 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
103 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
48 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
101 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
71 views

amplitude-phase modulation equations solution

I am trying to solve the following equation ...
2
votes
2answers
117 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
66 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
3answers
113 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 ...
-2
votes
1answer
66 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
48 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
40 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
31 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
61 views
0
votes
0answers
82 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
1
vote
1answer
55 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
44 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
vote
1answer
97 views

Help with plotting and improving code

I'm trying to solve a coupled DDE. Here is my code ...
0
votes
0answers
46 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
votes
1answer
63 views
0
votes
1answer
62 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
66 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} = ...
4
votes
2answers
81 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
votes
1answer
76 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 ...