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

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7
votes
2answers
148 views

Clicking phase plane with mouse

Here is what I have thus far: ...
3
votes
1answer
52 views

NDSolve with known tolerance function

I would like to solve the differential equation: y'[x]=F[y[x],x] with y[0.5]=y0 and x ...
0
votes
1answer
46 views

NdSolve problem :NDSolve::ndode: Input is not an ordinary differential equation

I am new to Mathematica. I am working on solving the following different equations numerically written in the code as below. Not so sure about the boundary values that depends on R (M(0)=0, n(1)=0) ...
2
votes
1answer
118 views

(NDSolve) Non-linear 2nd order ODE, regular singular point (looking for good methods for this problem)

I am solving this set of non-linear 2nd order ODE by NDSolve, $$r^2\frac{d^2f}{dr^2} = 2f(1-f)(1-2f)+\frac{r^2}{4}h^2(f-1)$$ $$\frac{d}{dr}\left[r^2\frac{dh}{dr} \right]=2h(1-f)^2+\lambda ...
2
votes
1answer
80 views

Nullclines and equilibrium point labels

I am trying to draw the vector field, nullclines, and equilibrium points for the system $$ \begin{align*} x'&=2x-y+3(x^2-y^2)+2xy\\ y'&=x-3y-3(x^2-y^2)+3xy \end{align*} $$ I have completed ...
0
votes
0answers
46 views

Having trouble reading this output (pure functions) [duplicate]

I'm after decoupling some odes and trying to solve them using mathematica but my output is in terms of Functions and InverseFuntions and I'm afraid I have no idea how to translate the output into ...
4
votes
1answer
63 views

How to use DSolve with vectors without decomposing into vector components?

Given a basic, two-dimensional ballistic trajectory problem, I can solve the equations of motion using DSolve (or NDSolve) by ...
2
votes
1answer
132 views

Coupled non-linear differential equations

I have a system of coupled nonlinear differential equations to solve: $$ \frac{\partial m(x,t)}{\partial t}+v(x,t)\frac{\partial m(x,t)}{\partial x}=-\gamma \frac{\partial^2 v(x,t)}{\partial x^2}, \\ ...
0
votes
1answer
71 views
1
vote
1answer
36 views

Value of event function not a real number

I am having some problems with handling an event during NDSolve. The event itself is simple, I am looking for when one of my coordinates, defined in ...
1
vote
0answers
76 views

Linear System with Complex Eigenvalues

My students will need to do the following work by hand. \begin{align*} x_1'&=-\frac14x_1+2x_2,\quad x_1(0)=1\\ x_2'&=-8x_1-\frac14x_2,\quad x_2(0)=1 \end{align*} They set it up in matrix ...
1
vote
0answers
49 views

Disease Network Model Using NDSolve

I have a basic disease model using NDSolve: ...
1
vote
1answer
65 views
0
votes
0answers
41 views

Two identical expressions for ODE, two distinct result

I have a problem in solving ODEs: two identical expression provides me different answers! I have no idea what's going on, can any one give me some reason why the following two expressions are ...
0
votes
0answers
47 views

Phase Portraits

If possible I want to create several phase portraits like this: ...
0
votes
1answer
38 views

Simplify huge output or using the output without showing it in full [closed]

I'm trying to solve a system of differential equations. It works fine but Mathematica creates a huge output, which, when shown in full, results in a file size about 100 mb. Using Simplify doesn't work ...
0
votes
0answers
79 views

Finding roots by solving its ODEs [duplicate]

Roots of fluctuating function (p,q real) needed to evaluate eigenvalues of $$ y(x) = \dfrac{\sin px }{p} + \dfrac {\sin q x }{q} =0 ...(1*) $$ form a real and complex infinite set. The way to ...
7
votes
3answers
281 views

Find the eigenvalues for an ODE

For example, say I have $y'' + \lambda y = 0$ and the endpoint conditions are $y'(0) = 0$ and $y'(\pi) = 0$. How can I find the values for $\lambda$ that for which there is a non-trivial ($y\neq0$) ...
1
vote
2answers
55 views

Using manipulate with a defined funtion to solve a ODE

As many in this community I'm new in Mathematica and while exploring the numerical solver for differential equations, I tried: ...
7
votes
2answers
292 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
99 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
77 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: ...
3
votes
1answer
134 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
102 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
101 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
74 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
52 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
72 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
31 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
84 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
172 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
42 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
49 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
302 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
49 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
117 views

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

I tried to solve system of ODEs, but something was wrong. ...
5
votes
2answers
82 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
95 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
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
54 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
37 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
76 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
104 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
111 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
52 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 ...