Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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8
votes
3answers
186 views

How to solve for the intersection points of two ellipses?

I have a parametric equation of two ellipses as follow $\begin{cases} x=a_1 \text{sin$\theta $}+b_1 \text{cos$\theta $}+c_1 \\ y=d_1 \text{sin$\theta $}+e_1 \text{cos$\theta $}+f_1 \\ ...
22
votes
3answers
964 views

Does Mathematica have a built-in tool that allows one to operate on both sides of an equation?

Geogebra has a very neat CAS view that allows one to solve an equation step by step in the following fashion: $\quad \quad \quad \quad \quad \quad \quad \quad \quad $ You type an equation and ...
0
votes
1answer
78 views

Solving non-linear ODE analytically in mathematica [closed]

I would like to solve the following differential equations $${dx\over dt}=\beta x-{{(C-x)^2}\over 4k} ,t\in[0, T]$$ where $\beta$,$C$ and $k$ are constant values. Also, the folowing terminal ...
21
votes
7answers
5k views

About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
1
vote
2answers
103 views

Find all roots of a function with parabolic cylinder functions in a range of the variable

I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...
1
vote
0answers
184 views

Solve set of non-linear equations with least-squares-fitting - constrain results?

I'm trying to solve a set of functions to determine the material properties from a set of measurement values. (To set up this method I just want to fit my model with some already calculated data). My ...
0
votes
0answers
23 views

Why does `NSolve` not solve this system of equations on a bounded domain?

I have three functions $E1,E2,E3$ of $t1$ and $t2$. The expressions are slightly complicated and involve trigonometric functions. For clarity purpose, they are given at the end of the question. I ...
1
vote
2answers
65 views

What is the role of the pattern object in this implementation?

In the documentation I found a nice idiom which allows me to do model fitting with interpolating functions. I think this kind of thing is amazing and a credit to the utility of an environment like ...
1
vote
1answer
122 views

Solve a system of non-linear equations

Is there any way to get an exact solution a system of non-linear equations? The system I would like to solve is: $\quad \quad \begin{eqnarray} h_{1}x_{1}=c_{1}\\ h_{2}x_{2}=c_{2}\\ ...
1
vote
1answer
125 views

Eliminating parameter from parametric equation [closed]

In Mathematica Online I tried: Eliminate[{x == t + t^3, y == t - t^3, z == 1 + t^4}, {t}] ...
2
votes
1answer
163 views

How to properly interpret a seemingly contradictory result in Mathematica?

I have a problem with interpreting the results of my notebook outputs. It is important that I do not err with the interpretation. Here is the full input: ...
1
vote
1answer
83 views

How can I solve an equation independent of a variable? [duplicate]

Let's say I have the equation $$ ax + b = 0 $$ and I'd like to find a solution that doesn't depend on $x$, so here the solution is obviously $a=b=0$. I could solve this using ...
2
votes
0answers
49 views

Problem with plotting a function that calls FindRoot

I am having difficulties in plotting the solution of FindRoot to solve 4 variables. I defined a function and then tried tp plot it, but got an error message ...
0
votes
1answer
417 views

Trying to solve a transcendental equation involving Bessel functions

I've never used Mathematica before and am trying to numerically solve equation (12) from this paper. Ideally I'd be able to find the smallest value of $x_{n\nu}$ for $\exp(-kr\pi)$ close to 1, and ...
1
vote
2answers
96 views

Why does Mathematica not evaluate the difference recurrence using `RSolve` or `RecurrenceTable`?

Mathematica does not evaluate the following recurrence of two variables using RSolve and only echoes the input: ...
0
votes
2answers
71 views

Solve returns empty list / running forever

Update: I made a mistake before and corrected the sign in code below in case people wonder what some comments mean. Thank you for those who answered. But I should have said that this is only part of ...
20
votes
4answers
3k views

How to get intersection values from a parametric graph?

I have this graphed: ParametricPlot[{2.4*Cos[t] + 1.6*Cos[3 t/2], 2.4*Sin[t] - 1.6 Sin[3 t/2]}, {t, 0, 4*Pi}] It is a star, and the lines cross each other ...
1
vote
1answer
108 views
0
votes
0answers
60 views

Inverse Superposition

There are 4 tables that, I have written them as bellow: (m, n, s, and r are orthogonal basis. r.r=n.n=m.m=s.s=1, and m.n=n.r=...=0). a's, b's, c's and d's are coefficients and are numeric values. ...
2
votes
1answer
127 views
1
vote
2answers
98 views

Solve[ ] doesn't work with transcendental equations

How to solve x^5-sinx=0 in mathematica? I try in this way: Solve[x^5 - Sin[x] == 0, x],but t doesn't work.
1
vote
4answers
3k views

How can I use assumptions with FindRoot?

I have something like FindRoot[f[x], {x, a}] Now I want FindRoot to constrain the solutions to 0 < x < 1. How can I ...
7
votes
6answers
454 views

Finding where two parametric paths cross?

I have been looking through other parametric equations questions and am still unsure where to start with this one. I am given two functions: ...
0
votes
3answers
76 views

Problems with finding the real solutions of equation

I am trying to find real solutions of equation using Mathematica 8.0 but there is some problem I don't know how to explain. For example, for the input ...
0
votes
1answer
37 views

Unexpected ReplaceAll behavior with NSolve

I ran into some unexpected behavior using ReplaceAll with an equation of motion using NSolve (or Solve, also). First solving for the initial velocity v0: ...
2
votes
2answers
78 views

Switching between solutions of a fourth order polynomial

I am plotting the roots of a fourth-order polynomial as a function of some parameter $r$ with the following code: ...
0
votes
0answers
54 views

Finding values of a variable fitting a function and minimizing a list of expressions

I am trying to implement bootstrapping (https://en.wikipedia.org/wiki/Bootstrapping_(finance)) of CDS curve. To implement it I am trying to minimize a series of expressions so that each expression is ...
0
votes
0answers
33 views

why is NSolve giving {y,x} in place of {x,y}? [duplicate]

Why is NSolve giving an inverse set of solution? Is it a problem with my computer only? ...
2
votes
1answer
107 views

How to Solve[] for rational constants?

I am trying to solve a system equations for rational, constant coefficients: ...
1
vote
2answers
99 views

Trouble using Solve and NSolve with functions involving Erf

I have the following functions: R[k_, x_, t_] := -.5*(k - x)*(1 + Erf[-(k - x)/t]) L[k_, c_, x_, t_] := .5*c*(k - x)*(1 + Erf[(k - x)/t]) I'm interested in ...
3
votes
1answer
105 views

Inaccurate answer for a system of equations

When I solve the following system of 6 equations by NSolve, it gives me an answer set; however this answer won't make the 2nd equation equal to zero (i.e. when I put the answers into ...
-1
votes
1answer
58 views

Find a minimum value which satisfies an equation

I have to find a minimum value of "a" which makes x=-a+b+c, y=-a+b+c^2 positive where a>1, 0 ...
4
votes
3answers
170 views

How do I generate a set of n-tuples containing integral solutions to a linear equation provided certain constraints?

Let $m,k,p$ be fixed positive integers. I want to create a table of k-tuples $(x_1,x_2,\ldots,x_k)$ comprised of solutions in positive integers to the equation below: ...
3
votes
4answers
143 views

How to merge permutations obtained from Solve on multiple variables?

When I compute the following expression to find integer solutions of the equation (x^2 + y^2 + z^2 == 14^2) ...
9
votes
3answers
147 views

How to find the solutions to $a+b+c+d=60$?

How can I find all the solutions to: $$a+b+c+d=60\quad (0\leq a,b,c,d\leq 30,\; a,b,c,d\in\mathbb N)$$ I've tried to use Solve[], but it says that there are more ...
6
votes
1answer
212 views

Solving $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$

I would like to solve the following equation: $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$ I have already posted it here, but still it doesn't work for me (I ...
0
votes
2answers
65 views

Solving two variable using two expressions each involving summation

I am trying to solve for h1 and h2 using function solve as in below code, Expression in solve has two equation each equates sum ...
0
votes
1answer
56 views

Complex Polynomial roots [closed]

I have the polynomial $p(z)=1-z^3$, I am using mathematica to get all three roots of $p$, say $a, b$ and $c$, obviously $$ 1-z^3=(z-a)(z-b)(z-c) $$ However, mathematica gives a wrong answer by saying ...
0
votes
2answers
51 views

Getting the first solution instance

How do I get Mathematica to stop a solver and give a result as soon as it finds the first solution instance? I tried this: ...
0
votes
1answer
55 views

Solve not returning anything

I have the following function: ...
0
votes
0answers
48 views

Sharp Ratio Maximization, Closed Forms

I am trying to get a closed form for the following first order conditions (n=4): Here's the nb-File. The code is as follows: ...
5
votes
1answer
105 views

Closed form of two-layer recurrence

I am trying to find a closed-form expression for $A(0)$, described by the following recurrence forms, as a function of $L$ and $d$: \begin{align} A(\ell) &= 1 + 2^d A(\ell+1) + \sum_{g=0}^{d-1} ...
0
votes
1answer
42 views

Trouble in finding instances of values of variables that satisfy an inequality

Consider the following mathematical expression with complex numbers (phasor) and two variables (lambda and ia2): ...
6
votes
2answers
175 views

Solving a two variable two equation trig expression

I am trying to use Solve to get what two angles (A and B) are in a problem I have. ...
0
votes
1answer
93 views

Plotting level curves for 2-variable exponential equation (Lotka-Volterra) - how?

I have $$\frac{e^{(d x + b y)}}{x^c y^a}$$ Incidentally, this is the energy integral for Lotka-Volterra as given by my lecturer's notes. I would like to draw the level curves for this equation for ...
12
votes
3answers
4k views

Find all roots of an interpolating function (solution to a differential equation)

I'm trying to find all the roots of the solution to a differential equation. Using NSolve or Reduce I don't get the roots, so I'm using an iterative method which I found in physicsforums.com. This ...
1
vote
0answers
69 views

How much time for solving a system of equations?

I wrote the following code for system of 11 equations; however when I run, it shows "Running" and has not converged to any answer after 2 hours. Please let me know whether it is normal or how I should ...