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

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5
votes
1answer
265 views

Solving an inequality that contains Log expressions

How can I solve the following inequality: Log[1/2 + c^2] > (1.4) (30^5) 2^(4.5) 9 (0.6) (2.8) (1 + Log[3]) (1 +Log[ Log[c + 1]]) ? I tried ...
5
votes
3answers
762 views

Solving a system of equations with conditions related to the number of solutions

The equation below describes a conic with oblique axis: $$9 + 22 x + 9 x^2 + 46 y + 24 x y + 16 y^2=0$$ It is a parabola, as the coefficients in $x^2$, $y^2$, $xy$ form a perfect square. To find the ...
5
votes
2answers
251 views

Solve for $a$ as a function of $\beta$?

I am trying to solve this equation: $$\beta^{-a} \Gamma(a) \sin(a \pi) + e^\beta \beta^{2 a - 1} \Gamma(1 - a) \sin(a \pi) = 0$$ I tried the following: ...
5
votes
2answers
2k views

Error (NSolve::ifun) when using NSolve, I need help interpreting the error

I wrote the following code to observe how the solutions to the equation $(e^{i a})^2 = e^{i b}$ varied as $b$ varied between 0 and $2\pi$ ...
5
votes
4answers
190 views

How to find a starting value that is closer to the solution?

I am trying to solve the following system. Firstly I have a table of numerical values I will call numbers ...
5
votes
2answers
506 views

Finding Points of Tangency of a Circle and a Parametric Curve

I have the following Parametric plot Generated from the following: ...
5
votes
2answers
525 views

How to find monotonically increasing intervals of a function

I tried this code, but not working Clear[f]; f[x_] := x^3 - 3 x + 2; ForAll[{x1, x2}, x1 < x2, f[x1] < f[x2]] Reduce[%, {x1, x2}, Reals] I expected the ...
5
votes
4answers
2k views

How to solve this logarithmic equation?

The equation $$x^2\cdot\log_2\dfrac{3+x}{10}-x^2\cdot\log_{\frac{1}{2}}(2 + 3x)=x^2 - 4+2\cdot\log_{\sqrt{2}}\dfrac{3x^2+11x+6}{10}$$ has two solutions for x, namely 1 and 2. I tried ...
5
votes
5answers
139 views

Non-algebraic equation in the set of complex numbers

The following equation in $\mathbb{C}$: $4z^2+8|z|^2-3=0$ is not algebraic and has 4 solutions : $\pm\frac{1}{2}$ and $\pm i\frac{\sqrt{3}}{2}$. The Solve function in Mathematica only returns the 2 ...
5
votes
4answers
917 views

An easier way to find the properties of an ellipse from its equation?

In this Q&A about fitting an ellipse to a set of points, there are multiple answers that generated general equations of the ellipse, like this one by @ubpdqn: However, the steps to find out the ...
5
votes
1answer
434 views

How to add equations' left and right sides together?

If we have two equations E1 and E2, and instead of using Solve to solve it, we simply need to manually add them up which would allow some simplification that could ...
5
votes
2answers
113 views

How to use ForAll to prove things about functions?

Suppose I first declare: $Assumptions = ForAll[{a,b}, b > a, f[b] > f[a]] I (wrongly, as it turns out) assume that that this would cause ...
5
votes
3answers
219 views

Finding the conditions for degenerate solutions to a cubic equation

I have a cubic equation (corresponding to the band structure of a physical system) given by w in the code below. ...
5
votes
3answers
390 views

Not able to get a solution to a Lagrange Multiplier Equation

I assigned several constrained optimization problems to my calc IV students to solve with Mathematica, but this one is being stubborn. The function to optimize is: f(x,y,z) = y Exp[x-z] with the ...
5
votes
2answers
318 views

Counting Real roots

I'm interested on how to count the number of real roots of a random polynomials in an instant, how to put the result in a table and how to plot it in a graph.I generated 1 million random polynomials ...
5
votes
1answer
3k views

Solving a system of linear equations modulo n

I have a system of linear equations $$ a+b+c \equiv 31 \pmod{54} $$ $$ 4a+2b+c \equiv 3 \pmod{54} $$ $$ 9a+3b+c \equiv 11 \pmod{54} $$ What should I input (I'm using ...
5
votes
2answers
451 views

Using RSolve correctly

I am having problems persuading Mathematica to solve even the simplest recurrence relations. As an example, how would you do the following? ...
5
votes
1answer
522 views

Using external variable as a variable inside WhenEvent & NDSolve

I'm trying to use the new WhenEvent functionality of NDSolve in Mathematica 9, in order to perform an action when a variable in the system reaches a certain value. I would like this variable to come ...
5
votes
2answers
3k views

Select Solution with real (positive, etc) coefficients - ignoring variables

I often need to solve equations for numerical coefficients while preserving numerous variables (e.g. to preserve scaling relations). Thus I end up with a set of solutions like $$ ...
5
votes
1answer
320 views

How can I tell why Mathematica returns no solution to this system of nonlinear equations?

I'm trying to solve a system of 12 equations and 12 unknowns with the code below. ...
5
votes
2answers
2k views

Solving a trig equation

I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ? ...
5
votes
2answers
129 views

Series solution of the Lane-Emden equation

I have the following problem: I'd like to show how the Lane-Emden equation would look like if someone would solve it as a series. Here's the code: ...
5
votes
1answer
212 views

Solution to $y = x^x (1-x)^{(1-x)}$ for $x$ [closed]

Does anyone have any insight to a symbolic Mathematica solution to this equation for $x$ in terms of y? Symbolic of any sort, just not numeric. $$y = x^x (1-x)^{(1-x)}$$
5
votes
2answers
306 views

Solve for x given an interpolation function, y

Given a list of data, lst={{x1,y2},{x2,y2},...,{xn,yn}} and the interpolation function fun, y=Interpolation[lst] which ...
5
votes
2answers
139 views

Initial time as parameter in ParametricNDSolve

I need a help with the function ParametricNDSolve. My goal is solve the equation \begin{array} &&\dot{x}(t) = y(t) \\ &\dot{y}(t) = x(t)-1-\varepsilon Cos(\omega t) \\ &x(t_0) = x_0\\ ...
5
votes
3answers
677 views

Equation is solved quickly using Solve but takes too long using NSolve

I have the following simple command to solve for h in an equation: Solve[(1 - 2.25577*^-5*h)^5.25588 == 0.9644952131579817, h] ...
5
votes
2answers
288 views

How to get $x$ in terms of $y$ and $w$ from $w = a p x^{p-1} \left(a x^p+b y^p\right)^{\frac{1}{p}-1}$

I'm having trouble to solve the following equation for $x$ both manually and in Mathematica: $\quad \quad w = a p x^{p-1} \left(a x^p+b y^p\right)^{\frac{1}{p}-1}$ In Mathematica notation: ...
5
votes
2answers
349 views

Why doesn't Roots work on a certain quartic polynomial equation?

In everything that follows I am using Roots to get the solutions to the equations. I start off with this equation: $$ \frac{A}{3}x^4 - x^2 + 2ax - b^2 = 0$$ Now ...
5
votes
2answers
219 views

Reduce with Integer domain, but receive a rational solution

Bug introduced in 6.0 and fixed in 10.0 I want to find the integer values $k$ so that D[f[x], x] has integer solutions. I tried ...
5
votes
2answers
475 views

Intersection of two splines

I have a collection of sets of points, each set defining the segment of a (nice) curve on the unit sphere $S^2 \subset \mathbb{R}^3$. The points are computed numerically. I now want to compute the ...
5
votes
1answer
163 views

$x^6-2\varphi^5x^5+2\varphi x+\varphi^6=0$ solving in radicals

How to solve the equation $x^6-2\varphi^5x^5+2\varphi x+\varphi^6=0$ in radicals using Mathematica? where $\varphi$ is the golden ratio. Solution is Ramanujan's Class Invariant $G_{125}$, Class ...
5
votes
1answer
405 views

Solving a nonlinear, second order d.e. in Mathematica

I am trying to solve the following differential equation $$ s''(x) = \frac{8}{9}s(x) -2s^2(x) + s^3(x), $$ with boundary conditions $s(-30) = 4/3 $ and $s(30)=0$, in Mathematica by using the following ...
5
votes
1answer
3k views

finding poles of a function

Is there a command to find the poles of a function $f=f(z)$? example: let $$f(z) = \frac{1}{z^2-1}$$ then we know that the poles are at $z=\pm 1$ but is there a special command in mathematica to do ...
5
votes
2answers
1k views

Find all roots in range

Is there any way to check for all roots in a range? Jens' findAllRoots function is pretty good, but runs at approx. 10% of roots missed when I ran a quick check on ...
5
votes
1answer
150 views

NDSolve solution violates initial conditions

I have the following code: ...
5
votes
2answers
253 views

How to “ReplaceAll” using a set of conditional expressions instead of a list of rules [closed]

Suppose that I have two linear functions f[x_] := f0 + f1 x g[x_] := g0 + g1 x and a (possibly rather complicated) set of conditional expressions, obtained ...
5
votes
2answers
473 views

Adding noise to nonlinear control system using NDSolve

I have a nonlinear control system ...
5
votes
2answers
303 views

Computing the sign of the real part of eigenvalues in a 3D linearized system with 3 parameters

So I have this dynamical system given by: $$ \left\{\begin{aligned} x' &= a(y-\phi(x))\\ y' &= x-y+z\\ z' &= -by \end{aligned}\right. $$ where $\phi(x) = \mu x^3 - \nu x$ and $a,b,\mu,\nu$ ...
5
votes
1answer
5k views

Can Mathematica help to rearrange an equation?

I have an equation which I want to rearrange so one variable is on the left side by itself. Normally, I would do this with basic algebra and identities. However, is it possible to use Mathematica to ...
5
votes
2answers
99 views

How to stop solving after one solution is found?

With[{P = 12}, Solve[{a^2 + b^2 == c^2, a + b + c == P, 0 < b <= a, c > 0}, {a, b, c}, Integers]] {{a -> 4, b -> 3, c -> 5}} ...
5
votes
2answers
148 views

How to find an estimated root efficiently with binary stochastic estimation of the function?

I am trying to construct certain nice geometric patterns, and one particular feature I'm trying to optimize is the balance of black and white corresponding to point being inside, or outside a ...
5
votes
2answers
551 views
5
votes
1answer
150 views

Solving an identity

I am trying to solve this identity using Mathematica: $$3 \sqrt{5 \sqrt[3]{37}-16}=\sqrt[3]{a}-\sqrt[3]{b}-c $$ I know that a, ...
5
votes
1answer
311 views

Calculate max value

Update Using ...
5
votes
2answers
854 views

Find all the integer numbers $a$, $b$, $c$, $d$, $e$, $f$, $k$ to this equation have three integer different solutions?

How to find all integer numbers $a$, $b$, $c$, $d$, $e$, $f$, $k$ that belong to interval $[-10,10]$, so that the equation $$\sqrt[3]{a x + b} +\sqrt[3]{c x + d} + \sqrt[3]{e x + f} =k$$ has three ...
5
votes
1answer
195 views

Find the domain in which a sequence converges

I seem to have a lot of problems in the format of: Given the sequence $a_n=\frac{n^\alpha+1}{2n^8+5}$, for $\alpha > 0$, find the values of $\alpha$ such that the sequence converges. However, ...
5
votes
1answer
671 views

Solving recurrence relation using Mathematica defined in a piecewise way

I have a recurrence relation defined as following: RSolve[ { p[0] == p0, p[1] == λ p[0]/μ, p[i + 1] == λ p[i]/(2 μ) }, p[i], i ] Note that the relation ...
5
votes
1answer
64 views

How to solve an equation system whose equations are based on Mod[x,y]

I'm trying to find the parameters of a specific linear congruential generator (pseudo random number generator) based on a list of the first five numbers generated by it. The list is this one: ...
5
votes
1answer
373 views

Use Pattern with Vectors in Assumptions

I had a problem using Pattern with Vectors in Assumptions. Here's how I use ...
5
votes
1answer
210 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, ...