Questions tagged [symbolic]

For questions about symbolic computation, as opposed to numerical computations.

Filter by
Sorted by
Tagged with
6
votes
2answers
135 views

DSolve does not return solution to simple system of second order PDEs

I'm trying to solve a simple system of second order PDEs with Mathematica 11.1. Here is the system: ...
2
votes
1answer
58 views

Concatenation of Distributions

I would like to calculate mean, variance, ... of a concatenation of distributions (is this the correct technical term?). For an easy example I am trying to calculate the mean of a PoissonDistribution ...
2
votes
2answers
125 views

How to solve these two differential equations

I have two differential equations and I try to use function DSolve to solve them together. ...
1
vote
1answer
75 views

DSolve does not work

I am trying to solve this coupled nonlinear pdes for $\kappa(x,t)$ and $\tau(x,t)$: where $\zeta_1 = \kappa(x,t)$, $\zeta_2 = 0$. I used this code ...
2
votes
1answer
50 views

Generate constraints that ensure positive definiteness

What is a good way to generate algebraic constraints that ensure matrix be positive definite? Ideally, I'd be able to do something like below ...
8
votes
1answer
94 views

DSolve leaks internal error messages when attempting to solve two first order autonomous ODEs

Issue reported to Wolfram, Inc as a possible bug in Version 12.1.1; CASE:4630268. With Mathematica "12.1.1 for Microsoft Windows (64-bit) (June 19, 2020)", ...
4
votes
1answer
187 views

How to show that ODE is Separable

I have an ODE: $$xy'= y+2x^3 \sin\big(\frac{y}{x}\big)^2.$$ I have to show that this is separable. I have introduced a function u = y/x. Then using ...
18
votes
3answers
342 views

Coordinate-free derivative

Given the function \begin{align*} f \colon \mathbb{R}^n &\to \mathbb{R}^n\\ v&\mapsto \dfrac{v}{\|v\|}, \end{align*} I would like to compute the derivative of $f$, that is $df(v)$. It is ...
2
votes
1answer
110 views

Two first order non-linear differential equation: Using DSolve to obtain the solutions analytically

I have two simple first order (coupled) differential equations which I denote as system together with its initial conditions ...
0
votes
2answers
52 views
2
votes
1answer
56 views

Three Coupled ODEs

I've been trying to solve it with Mathematica Order of DSolve but I'm not getting Anywhere! so if anyone got an idea i would be glad to tell me how to get answer p.s:I just want solution and Numerical ...
2
votes
1answer
135 views

How to symbolically solve this transcendental equation

The equation below shows up when dealing with geodesic curves on elliptic paraboloids: \begin{equation} u-c^2=u(1+4c^2)\sin^2\left(v-2c \ln\left(k(2\sqrt{u-c^2}+\sqrt{4u+1})\right)\right) \tag{1} \...
1
vote
1answer
66 views

calculate the flux of a vector field through a surface

How to calculate the flux of a vector field through a surface in mathematica? I've this field: F = (x, x^2 * y, y^2 * z) and this surface: ...
2
votes
2answers
82 views

How to Simplify expression efficiently inside Power

How can I simplify trivial expressions under the Power? Here is one example: (z2p-z2p z3)^-ϵ ...
2
votes
1answer
206 views

Solving a PDE (2D Laplacian) coupled with an ODE

I have asked this question before, but this is my new attempt and so instead of cluttering the previous one, I am making a new post. I am trying to analytically solve a PDE ($\nabla^2 T(x,y)=0$) ...
0
votes
1answer
68 views

Solving a coupled system of ODEs

I have two coupled ODEs for $T(x)$ and $t(x)$: $$\frac{d^2 T}{d x^2}-\beta (T-t)+K=0 \tag 1$$ $$\frac{d t}{dx}-\alpha(T-t)=0 \tag 2$$ $\alpha, \beta$ and $K$ are constants $>0$. Also, it is known ...
0
votes
0answers
43 views

Evaluating an integral with a long integrand either symbolically or numerically

I would like to calculate an integral with a very lengthy integrand. My script looks like this. ...
0
votes
0answers
74 views

Symbolic solution of differential equation with trigonometric initial conditions

We observe that D[Tanh[x3[t]], t] == Sech[x3[t]]^2 Derivative[1][x3][t] and that ...
2
votes
2answers
86 views

Symbolic properties of Re and Im

I want to define a function f such that f[x] is real whenever x is real. So I define ...
2
votes
1answer
55 views

How to get the result in terms of a previously defined expression?

Say I have a vector X[n_] := Table[Subscript[x, i], {i, 1, n}] and a matrix of connections: ...
4
votes
0answers
29 views

How does Simplify deal with contradictions in the assumptions?

Context Sometimes Simplify does generate a warning when the assumptions are self-contradictory. Take this example: ...
0
votes
0answers
33 views

Eliminate radicals from a symbolic expression

I get a lot of expressions of the type -(((11 + z) (13 - z + Sqrt[25 - 26 z + z^2]))/( 6 (-11 - z + Sqrt[25 - 26 z + z^2]) (7 - z + Sqrt[25 - 26 z + z^2]))) Which ...
-1
votes
1answer
339 views

How to write a more concise `RowReduce` function that can deal with symbolic matrix?

I asked a similar question in this post before and understand the reason why RowReduce function can't reduce symbolic matrix. I wrote an ...
0
votes
1answer
35 views

How to optimize a function with two variables such that the constraint is satisified

I have a hollow bar with outer diameter d1 and inner diameter d2. One end of the bar is fixed and the other is subjected load. ...
4
votes
2answers
75 views

Trouble verifying a solution to a differential equation

I am reading a physics book which has discussed one approach towards solving the differential equation $$ \frac{d^2 x(t)}{dt^2} = Cx(t) $$ as follows: Using Mathematica to solve the equation. I tried ...
0
votes
1answer
54 views

Solving indexed ODE in Mathematica

I would like to solve an ODE with indexed variables symbolically. Is there a way to do that? $$\frac{dp_{\beta\alpha}}{dt}=m\left(p_{1\alpha}p_{\beta2}+p_{2\alpha}p_{\beta1}\right)$$ m is called mass ...
2
votes
2answers
187 views

Laplace's equation with mixed boundary condition using separation of variables

The equation and boundary condition are defined in the picture where $T_1$, $T_2$, $T_3$, $k$ and $h$ are constant value. I am trying to use variable separation to solve the problem. If $T(x,y)$ ...
6
votes
3answers
387 views

Iterated differential operator

I would like to implement the following differential operator in Mathematica, $$ \prod_{j=1}^n \left({\mathrm d \over \mathrm d x}-j\right) $$ On a case by case basis, I can just expand it out and ...
8
votes
2answers
267 views

Two-dimensional Laplacian coupled with another equation leading to a BVP with integral bc(s)

I have the two-dimensional Laplacian $(\nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $x\in[0,L], y\in[0,l]$. On manipulating the second equation (which I have ...
5
votes
1answer
132 views

Derivative of real antisymmetric matrix in mathematica

Is it possible to find the derivative of components of a real antisymmetric matrix using index notation? Eg: I have a very large real antisymmetric matrix. Then from Matrix Cookbook, we know the ...
1
vote
1answer
143 views

Implementation of the general solution of Abel differential equation of the second kind in Mathematica

Introduction An Abel equation of the second kind in its canonical form is writen as $$y(x)y'(x)-y(x)=f(x)\quad (6)$$ for arbitrary $f(x)$. Despite the fact that this equation has general solutions 1 ...
3
votes
1answer
109 views

Issue with definite integration by parts using IntegrateByParts

I am trying to prove Cauchy's identity with Mathematica ResourceFunction["IntegrateByParts"]. It doesn't seem to work with definite integration. Cauchy's ...
5
votes
3answers
797 views

Integrating twice gives a different result than a double integral

I would like to compute the following double integral: $$ \int_{-1/2}^{0}\int_{-v}^{1+v} \frac{2}{1-(u^2-v^2)} dudv = \frac{\pi^2}{12} $$ When I do this using using ...
4
votes
2answers
84 views

Simplifying an expression containing inverse trigonometric functions

I somehow know that when simplifying the expression $$ \frac{2}{3} \left(2 \sqrt{3 B^2+4 J^2} \cos \left(\frac{1}{3} \cos ^{-1}\left(-\frac{J \left(9 B^2+8 J^2\right)}{\sqrt{\left(3 B^2+4 J^2\right)^3}...
2
votes
0answers
32 views

How algebraic (or more general) expression is represented (memory level, data structure) in Mathematica?

This is not a question about the usage of Mathematica, it is more about implementation. Mathematica is a very huge system, it can provide a series of very advanced operation against a Mathematica ...
2
votes
0answers
35 views

How to define a function based on an operation with parameters

I would like to define a function as the output of another operation depending on a few parameters. For example s[t1_,t2_]:= Integrate[t^n,{t,t1,t2}] s[0,1] I ...
1
vote
1answer
32 views

Should be a Piecewise function, a ConditionalExpression or Indeterminate, but it is a number

I apologize in advance for the lack of focus of my question. Consider the function: f[x_, y_] := x/(x + y); f[0,0] evaluates to ...
1
vote
1answer
108 views

Solving symbolic system of non-linear equations takes too long

I am trying to solve a set of system of symbolic non-linear equations: ...
3
votes
0answers
60 views

Convolution using the Laplace integral transform of certain functions

I am trying to convolve two functions: $f(t) = e^{- t}$ $g(t) = e^{-(e^{-t})^2}$ $(f*g)(t) = \int_{0}^{t} f(t-\tau)g(\tau) d\tau = \int_{0}^{t} e^{-(t-\tau)} e^{-(e^{-\tau})^2} d\tau$ Using the ...
12
votes
2answers
840 views

How to solve the Monty Hall problem?

Problem For purely recreational purposes I would like to solve the Monty Hall problem with Mathematica using the function Probability (dedicated to the calculation ...
1
vote
0answers
38 views

An apparent bug in Geometry`ConvexHull2

I was replacing some usages of Geometry`ConvexHull2 with ConvexHullMesh and found one of my tests failing. It turned out the ...
1
vote
1answer
22 views

Defining an iterated differential operator with compositions

I'm a bit new to Mathematica so this question might be a bit basic. Still, I could not find an answer. I wish to define a symbolic differential operator. Currently, I do something like the following: <...
2
votes
2answers
80 views

Slow replacement rule while combining symbolic summands

Edit: I attempted to use the method of repeatedly using Replace instead of ReplaceRepeated as suggested by Mr.Wizard, but the ...
1
vote
1answer
36 views

symbolic computation with any number of symbolic parameters. How to Simplify them?

I want to define d×d matrix $A$ as $A_{mn} = \exp{[\sum_{i=0}^m\sum_{j=0}^n \theta_{ij}]}$. Here $\theta_{ij} $ is real numbers. I wrote below script in Mathematica 12. ...
3
votes
1answer
79 views

Replacing symbols with numbers in a system of equations [closed]

I'm trying to simulate a physical problem through a system of linear equations in Mathematica. The system has a complete symbolic answer when the dimensions of the device are not evaluated but when ...
6
votes
3answers
220 views

Incorrect Result from DSolve for Diffusion IBVP?

The result of DSolve for the following IBVP doesn't seem to satisfy the IBVP: \begin{cases} u_{t} - ku_{xx} = 0 &\mbox{} k>0,x>0,t>0 \\ u(0,t)=p(t) &...
0
votes
1answer
31 views

Reducing large polynomial expression to product of simplar polynominals

A beginner to Mathematica. I am trying to express a large symbolic polynomial expression as a product of factors of simpler polynomials: For example I was able to factor this expression: ...
0
votes
1answer
42 views

Count heads: e.g. neglect all terms $\sin(x) \sin (y) \sin (z) \sin (w)$ for all values of the argument

I have a polynomial (functional) expression $E[F]$ in terms of a function $F$. I want to take an $F$-cube truncation in the sense that I want to and make terms of the form $F[w]F[x]F[y]F[z]$ vanish ...
16
votes
7answers
604 views

Missing solution - system of equations

Attention! This example already works as expected in Wolfram Mathematica 12.1.1.0 for function Solve. The problem was in version 12.1.0.0. Check out answer of Bob ...
3
votes
3answers
161 views

Inhomogeneous Heat Equation Formula Not Satisfying IVP

From Wikipedia, However, when I plug the formula of $u(x,t)$ into Mathematica 12.1, it doesn't seem to satisfy the PDE (does not give $0$): Here is the code: ...

1
2 3 4 5
23