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

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5
votes
2answers
88 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
96 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
48 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
58 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
39 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
88 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
108 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
117 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
53 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
103 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
76 views

amplitude-phase modulation equations solution

I am trying to solve the following equation ...
2
votes
2answers
136 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
79 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
67 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
119 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
68 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
49 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
51 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
32 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
66 views
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
21 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
66 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
61 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 ...
2
votes
2answers
110 views

Overdetermined System of PDEs

EDIT: Just to clarify a large part of my question is whether there is a way to make Mathematica solve a system with more equations than independent variables (so a system that is overdetermined but ...
1
vote
1answer
99 views

Help with plotting and improving code

I'm trying to solve a coupled DDE. Here is my code ...
0
votes
0answers
59 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
68 views
0
votes
1answer
66 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
89 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
92 views

Problem with ParametricNDSolve

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

Numerical error in DSolve [duplicate]

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

DSolve with Absolute Value

When playing around with DSolve, I enter the following: DSolve[{Derivative[1][y][x] == x + Abs[x]*y[x]}, y[x], x] The output is: $$y(x)\to e^{\frac{1}{2} (x ...
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 ...
1
vote
1answer
75 views

System of differential equation with delay

I try to solve this differential system with delay: ...
0
votes
0answers
39 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
2answers
129 views

Lotka Volterra Equation Plotting

So I have a basic Mathematica assignment where we need to numerically solve a Lotka-Volterra predator-prey population equation. So far I have managed to come up with this ...
3
votes
5answers
261 views

Taylor series without expanding factorial in denominator

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

Problem of WhenEvent in using variable updated in Event

equation1: value[inside RotationTransform] is a constant ...
2
votes
1answer
112 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
110 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
votes
1answer
45 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
106 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
114 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 ...
0
votes
0answers
46 views

DSolve gives back input (coupled ODEs)

I'm trying to solve a system of coupled ODEs, however I keep getting back the input whenever I try to solve with DSolve. The variables I'm solving for are complex. Here's what I have : ...
1
vote
2answers
43 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: ...