# Tagged Questions

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

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### What are the hidden specifications for FindRoot

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system" (or a nonlinear equation I suppose)...
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### $1 - \sqrt{5}$ $\in$ $\mathbf{R}$?

Why is there a difference in the output of the following codes? First: ...
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### How do I solve this equation?

I want to solve the equation $$f(f(-1)) = \sqrt{2} + g(f(2)),$$ where $$f(x) = \dfrac{a}{x^2} - 3x + 2, \quad g(x) = a\cdot \sin 2x$$ $a$ is unknown. The solution is $a \approx{-5.81}$. I tried <...
2k views

### Checking if the roots of a function are real

I'm trying to determine if the roots of a function are real. How would you do that? (In particular I'm interested in verifying that the roots of LegendreP[6, x] ...
2k views

### NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
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### How do I make Reduce yield all solutions explicitly?

Say I want to do the following: Reduce[ x+y+z==1, {x,y,z}, Modulus -> 7 ] then I get a solution with parameters, C[1] : ...
1k views

### Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
351 views

### Is there a relatively quick way to solve my integer-valued equation?

This is a very simple problem. It can be solved by nested Forloops that exhaustively test every possible case, throwing out all non-solutions. Find all the ...
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### Finding all points of period n in an iterated map

I'm trying to implement an algorithm of Jenkinson and Pollicott to calculate the Hausdorff dimension of a Julia set for the map $f_c : z\mapsto z^2 + c$. It's described on page 40 of their paper, ...
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### Combining solutions while solving

Here is a simple representation of my problem. I want to solve Solve[(w^2*c^2 /. #) - 1 == 0, w]& /@ {{c -> 1}, {c -> 2}} ...
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### 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 ...
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### Find the parameter values satisfying conditions for all roots of an equation

Hi I'm very new at Mathematica. My real problems concerns a much more difficult equation with many parameters, but I want to check that the method is good, so I made up a test equation. My test ...
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### Number of iterations in NSolve

In Excel's solver, one can define how many iterations are to be done, to one's liking. I am wondering if this is possible to do with NSolve in Mathematica? Code ...
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### 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 <...
2k views

### How to find the maximum value of an integer that satisfies some inequality

Consider the following Mathematica expression: Reduce[2^j/(j + 1) <= 10, j, Integers] which outputs: ...
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### 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...
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### 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 ...
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### Numerical solve question

Why does this work? Solve[5 Tan[t] + 9 == 0 && 0 <= t < 2 Pi , t] {{t -> π - ArcTan[9/5]}, {t -> 2 π - ArcTan[9/5]}} But this doesn't. <...
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### FindRoot kills kernel

Bug introduced in 7.0 or earlier and fixed in 10.1.0. I'm having problems with FindRoot killing the kernel. In my real application, I want to ...
447 views

### Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
281 views

### Using a Mathematica index as a DiscreteVariable in NDSolve when solving a coupled set of ordinary differential equations

Context Since the explanation below of the problem to be solved is lengthy, let me preamble this by saying that I have code that works to solve the problem, but I don't know whether (1) it's ...
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### Unexpected behaviour of Solve applied to two equations in two variables

I have a simple Mathematica expression Solve[{a(a-1)Sqrt[1+a^2+b^2] == b(a^3-1), b(b-1)Sqrt[1+a^2+b^2] == a(b^3-1)}] which returns (on version 8.0, and also ...
2k views

### Finding the number of solutions to a diophantine equation

I want to count total number of the natural solutions (different from 0) of the equation $2x + 3y + z = 100$, but don't know how. How can I calculate it using Mathematica? I tried: ...
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### 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) ...
786 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: ...
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### Efficient code for solve this equation

We have $a*b*c=-1$, $\frac{a^2}{c}+\frac{b}{c^2}=1$, $a^2 b+a c^2+b^2 c=t$ What's the value of $a^5 c+a b^5+b c^5$? I tried ...
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### How to find a tangent line with 2 points of tangency for a curve?

Say I have a function like this: f[x_] := 4 x^4 - 9 x^3 - x^2 + 10; Plot[f[x], {x, -1, 2}] It's obvious that there's a tangent line with 2 points of tangency ...
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### Why is FindInstance finding non-instances?

Consider this example: FindInstance[Exists[{x, y}, x > 1 && y > 1 && x > Sqrt[x + y]], {x, y}] which finds values of $x$ and $y$ such ...
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### How to correct this, f[a_] := FindRoot[eq == 0, {x, 0.5}], where eq contains a parameter $a$, without using eq[a]?

I want to solve an equation with a parameter $a$, and define the result as a function of $a$. It is something like this: ...
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### 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 ...
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### How to find the smallest root

I have a continuous, differentiable, monotonic, bounded function called F[t]. If t -> Infinity then ...
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### How to locate the position of a periodic orbit

These are the equations of the dynamical system ...
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### Why does Solve and Sum give different answers when according to Table it is the same sequence?

I have been thinking about a piece of code today, but I don't understand why I get different outputs from two in my mind similar Mathematical sums. First I observe that the Table command for this: <...
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### Why does Mathematica not give simple solutions to simple system of equations with powers

I trt to get Mathematica getting me the simple solutions for x and y from this system of two power equations: $$\text{Eq. 1: } z=x^{m}y^{n}$$ $$\text{Eq. 2: }z=\tau x^{m-1}y^{1-n},$$ The simple ...