# Questions tagged [symbolic]

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

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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: ...
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 ...
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. ...
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 ...
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 ...
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)", ...
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 ...
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 ...
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 ...
52 views

### Inverse function and Integral: How to simplify this DSolve output?

I'm trying to DSolve these equations with each other: ...
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 ...
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} \...
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: ...
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 ...
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 ($\nabla^2 T(x,y)=0$) ...
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 ...
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. ...
74 views

### Symbolic solution of differential equation with trigonometric initial conditions

We observe that D[Tanh[x3[t]], t] == Sech[x3[t]]^2 Derivative[x3][t] and that ...
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 ...
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: ...
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: ...
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 ...
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 ...
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. ...
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 ...
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 ...
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 $T(x,y)$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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}...
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 ...
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 ...
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 ...
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: ...
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 ...
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 ...
38 views

### An apparent bug in GeometryConvexHull2

I was replacing some usages of GeometryConvexHull2 with ConvexHullMesh and found one of my tests failing. It turned out the ...
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: <...
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 ...
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. ...
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 ...
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) &...
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: ...
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 ...
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: ...