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

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How can I get Mathematica to solve an equation with multiple variables?

How can I get mathematica to solve the non-homogeneous differential equation with undetermined coefficients listed below? Solve $\ y''(t)+3y'(t) = 2t^4 $, using: $\ y_p(t) = ...
6
votes
2answers
514 views

Alternate parameterization of a line

There are several ways to specify a line. In Mathematica's graphics, it is done by specifying two points and then connecting the points with the Line command. But ...
6
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2answers
380 views

Reduce and Solve unable to solve equation

I have the following equation. Why aren't Solve and Reduce able to find the solution? ...
6
votes
2answers
225 views

Using NSolve in the complex plane

I am trying to find numerical values for $\Im\ e^{\frac{1}{2} +i\ y} = \Im\ \zeta(\frac{1}{2} +i\ y)$ for a given range. I have tried: ...
6
votes
3answers
268 views

How to get the correct answer when solve this equation?

I want to find the values of the parameter $m$ to the graph of the funtion $$x^4 - 2 m x^2 + m + 1$$ has three extremal points make an equilateral triangle. I tried ...
6
votes
2answers
1k views

How to invert an integral equation

There have been numerous times when I've needed to invert an integral equation, i.e. I have something like $$f(x) = g_1(x)\int_{0}^x g_2(x') dx'$$ for arbitrary functions $g_1$ and $g_2$, and ...
6
votes
2answers
450 views

Very long Refine/Solve batch run - is my code broken, or just complicated?

So I'm trying to run some Mathematica code in batch mode from my university cluster. Specifically, I'm trying to find the equilibria of a system of ordinary differential equations. Inspired by the ...
6
votes
2answers
293 views

Why does Equal[“string”, False] not evaluate to False?

Why does Equal["string", False] not evaluate to False? I would have thought Mathematica could prove that these two things are ...
6
votes
2answers
1k views

Finding y given x from an interpolating function

I would like to put a dot on the point of a curve that has a specific y value but I don't know the x value. A simple example of my code is ...
6
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1answer
142 views

Why is FindInstance failing when I relax a set of constraints?

I'm attempting to use FindInstance to generate coordinate sets for plausible triangles with edge length distance constraints. E.g.: ...
6
votes
2answers
227 views

NSolve missing solutions in Mathematica 10

Running Mathematica 8.0.4 and 10.0.0 on a Windows 8.1 machine. Processed the same code with both kernels: ...
6
votes
1answer
547 views

How to Simplify equations over a Ring with Mathematica?

For example, when we work over a ring, the equation x^3=0 does not imply x^2=0 or x=0, but ...
6
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1answer
541 views

FindRoot options

I found an example of FindRoot usage that I couldn't find documented. It looks like: FindRoot[f[x] == 0.4, {x, 0, 1, 0, 1}] ...
6
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1answer
155 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 ...
6
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2answers
460 views

Solution of equation with power series (perturbation)

So I need to use Mathematica to find the solution of $y=x- \epsilon \sin(2y)$ as a power series in terms of $\epsilon$. I'd assume I'd need to create an equation $f=x-y- \epsilon \sin(2y)$, then ...
6
votes
2answers
109 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 ...
6
votes
4answers
318 views

FindInstance (and Solve, …) abysmally slow on a fully determined system of linear equations and inequalities: why?

I took a quick look for FindInstance and Solve-related questions but came up empty for the aspect that I am curious about. So ...
6
votes
1answer
296 views

Buggy Reduce/Resolve function?

It seems to me that this is a clear-cut case of Mathematica actually producing the wrong answer (with no warnings). I'm trying to express the fact that for any integer, there exists a factorization ...
6
votes
1answer
141 views

Recurrences of lists

Assume we have a multi-dimensional recurrence, e.g. $\qquad\begin{align*} a_1 &= (1,2) \\ a_n &= (1,2) + a_{n-1} \quad, n>1 \end{align*}$ with the easy solution $a_n = (n,2n)$. How ...
5
votes
4answers
1k views

How to find the sum all even numbers of this sequence?

I have a sequence $(u_{n})$ $$u_1= 1, \quad u_2 = 2, \quad u_3 = 3, \quad u_{n}= -u_{n-3} + 3u _{n-2} +2 u_{n-1}, \quad \forall n \geqslant 4.$$ I want to list the first $20$ terms of this sequence ...
5
votes
3answers
428 views

Solve for the intersection point of 3 surfaces

Basically, I have three 2-torus (tilted) in 3-dimensional Euclidean space. They are expressed by parametric equations: ...
5
votes
2answers
339 views

Equation solving with GroebnerBasis

I have a system of quadratic equations defined below ...
5
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6answers
414 views

Can someone help me solve this x*y*z=180

I have one question I've been trying for a while but I can't get the result for my equation.. So I've been trying hard but I can calculate only by hand but the problem is that I am afraid to miss any ...
5
votes
3answers
217 views

Solving $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}+\frac{3 W}{2}$ for $W$

When I solve the aforementioned equation for $W$ or $A$ on Mathematica I get a long and ugly equation in return, namely one of the solutions for $W$ is: (attempt to read at your own health) ...
5
votes
2answers
271 views

How to solve this combination equation?

I want to solve the equation $$ 2n\cdot\binom{n}{0} + 5(n-1)\binom{n}{1}+13(n-2)\binom{n}{2}+\cdots + \left(2^{n-1} + 3^{n-1}\right)\binom{n}{n-1} = 1685. $$ or using alternative notion for binomial ...
5
votes
4answers
374 views

Manipulating Equations

I would like to be able to manipulate algebraic equations. For example, let's say I enter 3x+5==2 I would next like to be able to manually subtract $2$ from both ...
5
votes
4answers
275 views

Symbolically solve and Plot equation involving Tan

I currently have the equation below for a beam with a hinge at various locations, the variable a can vary between 0 and 0.5. $$ Tan\left( {a\sqrt \alpha } \right) + Tan\left\{ {\left( {1 - a} ...
5
votes
2answers
288 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 ...
5
votes
2answers
240 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
1k 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
2answers
217 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
1answer
213 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
347 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
4answers
1k views

How to get exact roots of this polynomial?

The equation $$ 64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0 $$ has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
5
votes
4answers
1k 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
1answer
958 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
285 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
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2answers
2k 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
3answers
470 views

How do I find the intersection of a closed 3D curve given by numerical data with a specified plane?

I have a list of 3D data points which form a closed curve. My own data can't be easily generated analytically, but the qualitative behaviour is well represented by a parametric curve families such as ...
5
votes
1answer
318 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
1answer
914 views

How Can I use Solve/Reduce Output

Suppose I want x and y to be rationals Solve[ x^2 + y^2 == 1, {x, y}, Rationals] I am ...
5
votes
1answer
199 views

How to substitute the following conditions into an expression?

I have an expression: $p=a\;b\; x + b^2\; y + a\;c\; z$. I want to substitute $a\;b=1$, $b^2 = 2$ and $a\;c = 4$ to obtain $p = x + 2y + 4z$. How can I tell Mathematica to do that? I dont know how to ...
5
votes
2answers
1k 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
250 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
275 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
2answers
124 views

What are the Method options Solve command accepts?

What are the Method options Solve command accepts? Solve has the Method option, however documentation contains no methods that it accepts...
5
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1answer
373 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, ...
5
votes
1answer
94 views
5
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2answers
180 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
282 views

Adding noise to nonlinear control system using NDSolve

I have a nonlinear control system ...