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

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0answers
368 views

differential equations with implicit functions

I have an ordinary differential equation that contains coefficient functions that depend implicitly on the independent variable via an algebraic equation. I am trying to go ahead and use NSolve to ...
2
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0answers
164 views

Why is FindRoot initial value far from the specified one?

I am trying to numerically find the root of a function that looks a bit like: 1/x - (SchurDecomposition[A[x]][[2]])[[1]], where ...
2
votes
0answers
190 views

Solving $k\log(n) - k\log(k) \leq u$

How can I persuade Mathematica to help me find solutions to the inequality $k\ln(n) - k\ln(k) \leq u$ over the reals, assuming $u \geq n \geq k \geq 1$. When I evaluate ...
2
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0answers
231 views

Am I entering this 2-variable recurrence correctly?

I'm trying to solve this recurrence with two variables. ...
2
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0answers
309 views

FindRoot - Speed and errors

I am using FindRoot[] to solve a complicated equation. It seems I get the correct answer even though I get errors about an ...
2
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0answers
99 views

Why cant Mathematica solve this equation? [duplicate]

Possible Duplicate: Can Reduce *really* not solve for x here? Why cant Mathematica solve this equation? ...
2
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0answers
425 views

Numerically/Analytically Solving a System of Equations

I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
2
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1answer
478 views

Inconsistent initial and boundary conditions

I have a 4th order nonlinear PDE with the following BCs and IC: ...
1
vote
4answers
2k views

Solve trigonometric equation

I'm looking for a solution (graphic, numeric or analytic) for a function of the form: $$a^2\tanh(x)=\tan(ax),\quad a ≥ 1,\ x > 0$$ preferably using Mathematica. Any advice?
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3answers
81 views

Getting a list of x coordinates of intersection points of two functions

I have two functions, f[x_] := 5 Sin[2 x] g[x_] := (5 x + 2)/(x + 2) I am trying to find the x coordinates that intersect ...
1
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3answers
327 views

TrueQ - Test of inequality [duplicate]

I want to look if a term is <0,>0 or ==0. What is wrong when I write ...
1
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4answers
143 views

Solve reports it can't handle my equation

I am trying to solve the following equation Solve[x ϵ + (-ϵ) x^-ϵ - c (-ϵ) x^(-ϵ - 1) == 0, x] Yields Solve::nsmet: This system cannot be solved with the ...
1
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1answer
2k views

Solving functional equations in Mathematica

I am trying to solve functional equations in Mathematica, but got nowhere. Just a simple example: $$f(x+y)^2=f(x)^2+f(y)^2$$ for all $x,y \in R$, assuming f is a real-valued function. How should I ...
1
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1answer
206 views
1
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3answers
200 views

Plot a table of ranges

I have table with values like: t = {1.234 <= a <= 2.345, 3.42 <= a <= 5.67, ...} and I want to plot this table, the ...
1
vote
2answers
272 views

Is there a better way to get the eight points of intersection?

I want to get the eight points of intersection from the equations 2 Abs[x] + Abs[y] == 1 and Abs[x] + 2 Abs[y] == 1. To solve ...
1
vote
1answer
815 views

How can I understand the result Mathematica returns from DSolve?

I have solved an ODE using DSolve, but I have a problem with understanding the solution. In general the solution is in the form: ...
1
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1answer
138 views

Simple rule appears not to work

I have the following simple code ...
1
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2answers
373 views

solving for one solution to a system of polynomials

I'm trying to solve a system of equations: ...
1
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4answers
200 views

How to extract only real solutions from the result of Solve

For Example, I have the following polynomial equations: $$ \left\{ \begin{array}{ll} \dfrac{2025 (208 x+5 (y-3446))}{52 (y+90)^2}+\dfrac{300 (8 x-21 y+1920) (y-80)}{7 (x+30)^3}+\frac{300 (80 x-21 ...
1
vote
4answers
299 views

Calculating difference ratios (Δβ/Δρ) from a data set

I am little bit confused about how to calculate δβ/δρ value if I have set of values like this. I have the values of β and ρ like this. ...
1
vote
3answers
368 views

How to find intersection points of lines?

Considering I have three functions f1 = -x + 1; f2 = x - 1; f3 = x + 3; How can I find the intersection points of this functions? Thanks. This didn't work ...
1
vote
2answers
554 views

Why do Solve, NSolve, and FindRoot all fail on this simple, solvable actuarial equation?

If we express conditional mortality as a vector of annual probabilities of death, like so ...
1
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4answers
353 views

How do I create a list of 25 random quadratic equations in the form ax^2+bx+c?

My teacher suggests using the RandomInteger command along with the Factor command, but I cannot figure out the syntax. A, b, and c need to be non zero integers between -10 and 10.
1
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3answers
532 views

How can i get the solution of complicated equation?

This is the equation about zeta. NSolve[eq] could not solve this equation. (I think it is too complex to solve by NSolve.) I ...
1
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2answers
2k views

Using FindRoot with an interpolating function

This question bears resemblance to a few other questions on mathematica.SE about finding points of intersection of crossing curves. I know that the guidebook of numerics has an entry about the whole ...
1
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3answers
136 views

Find value of x such that x! less than or equal to 1000

I am trying to find the maximum value of $x$ such that $x! \leq 1000$. I tried the following: NSolve[Factorial[x] - 1000 == 0, x] but I got this message: ...
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2answers
67 views

Solutions to multivariate equation

Is there any way to get Mathematica to give a set of solutions (pairs of x and y that are integers) to an equation with multiple variables? Something like: ...
1
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1answer
313 views

Why my differential equations become True? [duplicate]

I've been trying to solve a system of nonlinear differential equation, but the conditions are a bit weird. Two of the differentials equate to the same equation, but have different boundary ...
1
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2answers
314 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...
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1answer
443 views

2 non-linear equations with 2 unknowns which I cannot solve

I have the following equations and I would like to solve them in Mathematica anyway. Numerical results are very much welcomed. However, when I use the command ...
1
vote
3answers
1k views

Conditional expression

How do I evaluate a conditional expression in order to convert the solutions that are in terms of $x$ to a new variable $c$ depending on $x$? The conventional method I have been using with eliminate ...
1
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3answers
94 views

Finding roots of transcendental equation and collecting into a list

I am working on a physics reserach project for school and I have run into some troubles working Mathematica. I am a fairly inexperienced mathematica user so any help would very much be appreciated. I ...
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2answers
122 views

Solving for the limits of an integral

I am trying to get Mathematica to solve for the symmetric limits of an integral of a Square Wave. ...
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2answers
113 views

Why does this expression take a long time to evaluate?

I was just wondering whether there's an easy to see reason for this expression to take a very long time to evaluate: ...
1
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1answer
145 views

FindMinimum and NMinimize to solve equations

I know that I'm not a Jedi in solving Equations and minimizing functions; but now I've this problem, and the solution is far to me. I want to solve this equation: ...
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1answer
124 views

Unexpected result from FullSimplify

In the following simplification why doesn't Mathematica get a zero when asked to compute "Y-Z" eventually? ...
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2answers
754 views

Solve within a range?

Is it possible to solve an equation in which some some of the parameters have defined ranges? Example: ...
1
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2answers
466 views

Projection of curve 3D (x,y,z) on the x-y plane

I have a following systeme : \begin{equation} \left\{ \begin{array}{rcr} (\beta+\frac{1}{2}\delta^{2})\nu_{1}(u)-\delta\nu_{2}(u)+\nu_{3}(u)& = &0\\ ...
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1answer
226 views

Help to solve exponential equation over positive integers

I am trying to solve the equation $\frac{4}{9} = \big( \frac{1}{3} \big) ^n + \big( \frac{1}{3} \big) ^m $ with $n$ and $m$ both positive integers. I type into Mathematica the following In:= ...
1
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3answers
151 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) ...
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1answer
457 views

Substituting solution from Solve into the equation and making a plot

I want to solve an equation and substitute it into a Plot expression. My code looks something like this a[b_, x_] := bx + 1; sol = Solve[(1 + b)x + 1 == 0, b] I ...
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3answers
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 ...
1
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1answer
573 views

Comparing two symbolic expressions

Does Mathematica provide any way to compare two symbolic expressions and find which is the greatest? For example, I want to find which is the greatest of ...
1
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2answers
455 views

Replacing variable in an equation with an Interpolating function polynomial and plotting residual

I was trying to plot the residual for the solution of my PDE. However, I was unsure about a couple of things. I imported the data and created an Interpolation polynomial with ...
1
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1answer
862 views

FindRoot inside Table

(MWE at the end of the post) I need to solve a non-linear equation $f(y;x_1,x_2,..,x_5)$ in one variable $y$ and then compute 4 new output expressions, for over 60 different initial parameter inputs ...
1
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1answer
83 views

Improving Performance - Finding Polynomial Roots [duplicate]

I'm fairly new to Mathematica. In the past, my usage has mostly been limited to solving the occasional equation, making some plots, and working with small scaled statistics. None of these have been ...
1
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1answer
194 views

NSolve fails to solve a nonlinear equation

Mathematica can not solve this: g = 9.82; ω = 0.5; h = 5; y0 = 1; v = 0; τ = 0; NSolve[h + v t - (g t^2)/2 == y0 Sin[ω t], t]; The error code is: ...
1
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1answer
195 views

solve recursion equation with condition

How can I find $f(x)$ in terms of $x$ in the following equation? $ -k\, x \,f(x) + k \, (x + 1)\, f(x + 1) - r \, f(x) + r\, f(x - 1) =0$ $r$ and $k$ are constants and $f(x)$ should satisfy: ...
1
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2answers
125 views

Problems with Solve when constraining solutions to a range

I have the following code ...