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

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5
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0answers
81 views

Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite ...
6
votes
1answer
169 views

The third argument of the Root function

Consider the roots of an arbitrary indecomposable polynomial: sol = Solve[x^5 + 2 x + 1 == 0, x] The returned expression is ...
1
vote
1answer
195 views

Solving an exponential multivariate equation

I have the following equation: p = 1/(1 + E^(-51.179 + 0.849 x1 + 2.3649 x2 + 1.155 x3 + 1.46 x4 + 1.31 x5)) and I want to find the set of values for x1 to x5 ...
0
votes
1answer
163 views

How to return the rhs of a transformation rule from within Compile[]

I have defined the following function: ...
0
votes
1answer
230 views

Solve[polynomial, x, Reals] doesn't get all real roots or correct ones?

My main confusion is about the difference between the two code blocks at the end of this long spiel, but the spiel contains the code to create the polynomial if its coefficients are helpful for ...
0
votes
1answer
125 views

Manipulating and using result of DSolve

I have an unsightly looking equation that nonetheless has an analytical solution. The solution is ugly as hell, but exists; I use the following code with the DSolve ...
3
votes
1answer
202 views

When does the real part of Zeta vanish on the critical line?

This seems to be a quite a simple problem but I cannot make it work. I am trying to find all values within a given range for which the real part of the Zeta function vanishes on the line: ...
1
vote
3answers
150 views

automatic processing of numerical results in `Plot`

First I want to solve an equation $F(x,y)=0$ for $y$ by supplying a value of $x$. (suppose obtaining the analytic form of $y(x)$ is too difficult) Then I want to plot root $y$ (numerically calculated) ...
1
vote
1answer
897 views

Singularity / stiffness / precision errors with NDSolve

I have a relatively simple 2nd Order ODE problem I'm trying to solve numerically $p'' + \frac{1}{r}p' = A(\frac{p(r)}{p(r) + k_{m}})$ where $A = 7.5795*10^9$ and $k_{m} = 1$. So trying to get ...
1
vote
0answers
38 views

How can I access numerical values of variables calculated with Solve? [duplicate]

I am trying to calculate some thermodynamical cycles so I often use lists with equations. Here's a simple example: ...
1
vote
2answers
192 views

Setting up and solving system of equations

Consider the following code: ...
1
vote
2answers
157 views

ReplaceAll a list of rules to an equation

Given the following equation and rule, how would I Solve the equation for tr, k and ...
0
votes
1answer
393 views

Solve the quadratic equation? [closed]

I can't seem to solve the general quadratic equation: Solve[ax^2 + bx + c == 0, x] Out[299]= {} It just outputs the empty list. How do I solve this equation?
0
votes
2answers
94 views

Gaps in plots of equation solution from parameter

I'm trying to plot solution of system of equations as a function of parameter ...
1
vote
1answer
112 views

Passing f[x][[1]] to FindRoot [duplicate]

FindRoot seems to fail for most examples of the form f[x_?NumericQ] := {x - 3 , x^3}; FindRoot[f[x][[1]], {x, 3}] ...
0
votes
0answers
87 views

DSolve is rejecting my description of a system of PDEs

I am trying to solve a system of partial differential equations using DSlove. But i get the input equations in return. Dsolve is not doing anything ...
1
vote
3answers
385 views

Can plot a function, NSolve takes too long

I'm new to Mathematica, so maybe mine is an easy to solve issue, but I haven't been able to figure it out. I have a series of linear ODEs I solve using for: ...
-2
votes
1answer
155 views

Proof: Convergence of an equation and show the first derivative is bounded

We have the following equation \begin{equation} x(k+1)=\arccos\bigg( -\frac{1}{2(Dr^{\frac {|\sin(2x(k)+\theta)|}{M\sin x(k)\sqrt{A+2B\cos(2x(k)+\theta)}}}+1)} \bigg) \nonumber \end{equation} ...
0
votes
1answer
155 views

Defining a curved region for NDSolve

I have an equation to solve using NDSolve which involves two parameters: $en$ and $k$. The equation produces a set of curves when $en$ is plotted against $k$. In ...
1
vote
1answer
242 views

Plot the solution complex transcendental equation

I'm trying to plot an implicit function satisfying a complex transcendental equation. The code is the following: ...
3
votes
3answers
198 views

What is the formula for this numerical series?

I'm developing a questions game. My goal is that the score for each correct answer will increase as the user answers more questions. Initially there are 15 points for each correct answer. Every 4 ...
6
votes
2answers
119 views

Why is ToRadicals[] not able to handle all cases? Is there a workaround?

The documentation for the function ToRadicals says: ♦ There are some cases in which expressions involving radicals can in principle be given, but ...
0
votes
1answer
420 views

How to change machineprecision digits

I am trying to compute t0: ...
17
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 ...
5
votes
2answers
320 views

Optimum number of cog teeth for two step helical gearbox

Note: Cross-posted at http://community.wolfram.com/groups/-/m/t/137895?p_p_auth=8QnKtT9I. I am to design a two step gearbox. The first step is to choose the number of teeth in each cog wheel in ...
4
votes
3answers
434 views

How can I get the exact solution of this equation (inequality equation)?

I want to solve the equation and inequality equation $$\sqrt{8\cdot 16^x - \dfrac{1}{2}\cdot 9^x }= 3\cdot 4^x - 3^x$$ and $$\sqrt{8\cdot 16^x - \dfrac{1}{2}\cdot 9^x } \leqslant 3\cdot 4^x - 3^x.$$ ...
8
votes
3answers
741 views

Can Mathematica solve this sort of functional/differential equation?

I am looking for differentiable functions $f$ from the unit interval to itself that satisfy the following equation $\forall\:p \in \left( 0,1 \right)$: $$1-p-f(f(p))-f(p)f'(f(p))=0$$ Is there a way ...
4
votes
3answers
209 views

Why the inequality does not take into account the domain?

I have this inequality: Reduce[(4000-1000k)/(k-4) < 0] and the answer is k ∈ Reals I would expect ...
0
votes
2answers
611 views

Classification of a linear system of equations with a parameter

I need to get every possible value of k that returns infinite number of solutions or no solution to this system: ...
5
votes
1answer
306 views

Use Pattern with Vectors in Assumptions

I had a problem using Pattern with Vectors in Assumptions. Here's how I use ...
4
votes
2answers
327 views

Find the value of parameter so that the equation has one solution

Let $(E_l) : x^4-4x^3+x^2(5-l^2)+4 x l^2-4l^2 = 0$ be an equation with $l$ as a parameter and $x$ as an unknown and $S_l$ the set containing all the real solutions of $(E_l)$. Then there is a unique ...
2
votes
4answers
391 views

find the number of integral solutions a+b+c+d+e+f = 18 [duplicate]

Find the number of integral solutions of a + b + c + d + e + f = 18 where a, b, c, d, e, f are elements of the range ...
2
votes
0answers
122 views

Equation Solving: Solution in terms of predefined functions

Is there a way that I can have Mathematica give me the solution of a problem it has solved in terms of functions that I have predefined? The specific problem I'm trying to solve is: ...
3
votes
1answer
315 views

How to find the roots of an equation which is almost singular everywhere

I'm trying to find the roots of the equation as a variable of k: ...
3
votes
3answers
882 views

Implementing Newton's method

I have this question on coding Newton's method in Mathematica. I have some code to go by but I have no clue if it's computing the functions in the right order. The book is the numerical methods ...
1
vote
3answers
297 views

TrueQ - Test of inequality [duplicate]

I want to look if a term is <0,>0 or ==0. What is wrong when I write ...
0
votes
1answer
608 views
1
vote
2answers
290 views

Approximate solution to system of polynomial equations

I'd like to solve approximately the following system of equations for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$ all real and nonzero: ...
0
votes
1answer
69 views

LMS distance from a point to an InterpolatingFunction

I have a short script to NDSolve a second-order nonlinear BVP, which as its output produces an InterpolatingFunction object. I ...
0
votes
0answers
164 views

System of integral equations with integrals on both sides

I'd like to solve the following equation numerically for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$: $\displaystyle\int_0^{\infty}\Big[L_1\Big(\frac{k^2}{2}\Big)\Big]^2e^{-k^2}L_m(k^2)\ dk=$ ...
2
votes
3answers
263 views

Minimization problem

How could you find the smallest constant $c$ that satisfies $$\frac{3^{3k}e\sqrt{3}}{\pi\sqrt{k}\;2^{3/2+2k}} \leq 2^{\;c\;k}$$ assuming $k\geq 1$ is an integer. You can of course take logs of ...
1
vote
0answers
114 views
5
votes
1answer
181 views

Verify Harmonic Addition Theorem with Mathematica

I've calculated the harmonic addition theorem and would just like to check my result with Mathematica. However, ...
3
votes
1answer
242 views

Minimizing a potential using Solve

I am having problems minimizing a potential: $\text{V}(h,\eta)=\gamma \left(-h^2\right) \left(\eta ^2 \cos ^2(\theta )+\eta \cos (\delta ) \sqrt{-\eta ^2-h^2+1} \sin (2 \theta )+\left(-\eta ...
0
votes
0answers
112 views

Mathematica returns different results when requested by Reduce, Solve [duplicate]

When I request with Reduce, Mathematica returns: ...
2
votes
1answer
722 views

Nonlinear least squares

I have a typical nonlinear least square problem and it seems very similar to the example provided in the section on parameter fitting at the Wolfram website. Unfortunately I always get some error ...
3
votes
2answers
594 views

FindFit for a differential equation model with multiple variables?

I'm trying to figure out how to use FindFit with a multivariable differential equation model and data. I've successfully made it work for the one-variable version ...
0
votes
1answer
164 views

Solve doesn't return all solutions [duplicate]

I got a simple cubic equation as input, but Mathematica does not give all solutions, why is this the case here? ...
1
vote
1answer
149 views

Minimum value with two factors

Approximate the minimum value of $2e^{x-2}-6x+xe^{x-2}$. Is my input correct? If not can you please correct it? ...
6
votes
1answer
521 views

Issue with NSolve

I defined the following function: sw[ θ_, ϕ_, h_] = 1/2 Sin[2 (ϕ - θ)] + h Sin[ϕ] Based upon whether I use Solve or NSolve, ...