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

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Use Solve[] with Bessel, Gamma, and HyperGeom functions?

I need to find values of {a,b,c} such that the 0th, 2nd, and 4th order moments of f[x]=Exp[-ax^4 - bx^2 - c] will equal respectively {1,2,10}. I didn't really expect this to work, and it didn't: ...
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0answers
6 views

solving non-linear set of equations using NSolve in order to get all roots

vpw = 3.3 Mp = 80 rp = 0.014*Mp b0 = 26.31016273 - (1.7168*10^3/t) - 3.5519*Log[t] b1 = 24.65681838 - (1.547*10^3/t) - 3.4314*Log[t] b2 = 9.080370819 - (6.9445*10^2/t) - 1.2222*Log[t] g = b0 + ...
4
votes
2answers
417 views

Order of a pole

Is there a simple way to determine the order of the poles of a rational function? I have a difficult function where I need Mathematica to find the poles. It would be interesting to also know what the ...
0
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1answer
103 views

In which condition releated to thee coefficients some equation has a solution

Please excuse me if the question seems to commonplace. Can Mathematica give a response to this question: In which condition related to the coefficients $c>0, \, n\geq 2, 0<p<1,\, a>c$ ...
2
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1answer
126 views

Visualizing how the zeros for this function change as its input parameter changes?

I'm trying to explore how the zeros of a certain parameterized function change as its parameter changes. ...
0
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1answer
28 views

Finding solution of equation with differentials [on hold]

I am trying to find the point of maximum exponential curvature, where the exponent equation is: y = 0.2e^(0.4x) I know the equation for this point is: k = y'' / [(1+y')²]^(3/2) How can I code this ...
0
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0answers
67 views

Numerical solution to integral equation [duplicate]

I have an integral equation where one factor $f(t)$ in the integrand is defined in terms of an integral equation where it is again a factor. $\quad \quad y[t]=\int _0^tf[\tau ]g[t-\tau ]d\tau + ...
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1answer
26 views

How do I assign the solutions of an equation to separate variables? [duplicate]

I'm a beginner to Mathematica. Here's my question. I'd like to store the output(s) of a Solve command to variable(s) that can be manipulated later. For example, I would like x1 and x2 to be the two ...
2
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1answer
64 views

Exclusions found but Solve and Reduce don't find exclusions

I have the following from Stan Wagons Mathematica in Action. ...
1
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1answer
50 views

Reduce with for all and implies

I have the following question. p1 = a (1 - c + a) p2 = b (1 - c - b)/((1 - b)^2) v1 = (x^1.5 - 3*x)*p1 v2 = x*p2 I want to find x ranges which makes v1>v2 under ...
4
votes
1answer
118 views

Dealing with 6 VERY large equations. Am I doing this correctly, and can I expect a solution?

I'm new to Mathematica, but so far, everything seems straight forward and intuitive, which is really nice. However, I've come to use this software since I have to show a rather nasty 3x3 matrix is ...
4
votes
1answer
106 views

Finding and plotting roots with parameter

I have the following function: $$u(x,t)=\sum_{k=1}^\infty\frac{v_0 L}{\lambda_k c \sin\left(\lambda_k\right)}\sin\left(\frac{\lambda_kx}{L}\right)\sin\left(\frac{\lambda_kct}{L}\right)$$ and this ...
2
votes
1answer
32 views

“Reduce” an expression in terms of a sub-expression

Newbie here. I've been trying to use Reduce to solve a rather long equation. The evaluation has been running for more than hour now, but still hasn't stopped. I've got an inkling that if I were to ...
9
votes
2answers
468 views

Is there a way to symbolically invert a piecewise function

I have a piecewise function that is continuous and strictly monotonic, like this: f[t_] = Piecewise[{{t/4, t < 0}, {t/2, t < 3}, {3/2 + (t - 3)*3, True}}] ...
0
votes
1answer
61 views

Why does this evaluate to {}?

I'm stuck with what seems to be an extremely simple issue, still, I just can't seem to find the solution or even the cause of the problem. So my issue is that I have the following surfaces: ...
5
votes
2answers
78 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}} ...
3
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1answer
64 views
0
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1answer
60 views

Solving an NODE in series

How can I solve this NODE in series y''[x]^2 + (1/2)*y'[x] + (1/2) y[x] == p x + q. `p` and `q` are constant. But do not know how to actually solve it with ...
13
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1answer
312 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an ...
2
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0answers
45 views

Is FindRoot wrong about its WorkingPrecision?

I noticed an odd mismatch between the behaviors of NDSolve and FindRoot. If you give NDSolve an equation of a certain precision, say 20, and tell it to use a higher WorkingPrecision, say 30, it will ...
0
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1answer
49 views

Solving a differential equation with multiple coefficients [closed]

I have a syntax problem solving a differential equation in Mathematica (10th version). The input for the equation I need to solve is as follows: ...
4
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1answer
271 views
0
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0answers
43 views

Optimal way to search for Fibonacci $≡−1 \pmod {p^2}$ [closed]

I came upon this question, and see a few people brute force searching for a prime $p>3$ such that the Fibonacci number $F_{np}≡−1 \pmod {p^2}$ for some natural number $n$ I was wondering how ...
0
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1answer
49 views

how to simplify -1 to shared power (produced by Solve)

I want a real solution to look real. But this solution does not: ...
9
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0answers
102 views

Strange result of Reduce and ForAll

In the question Can Mathematica tell me if a polynomial has all real roots?, quite a few of interesting answers were given. I wanted to add another one, using quantors, and observed some strange ...
3
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1answer
70 views

Solve problem: Inconsistent or redundant transcendental equation

I would like to mechanically Solve[a y == (1 - a) x && u0 == x^a y^(1 - a),{x,y}], given 1>a>0 and u0>0. The emphasis is on mechanically: I know it is ...
5
votes
2answers
122 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
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 ? ...
-1
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0answers
61 views

Solving a general equilibrium model gives blank output [closed]

I'm trying to solve a general equilibrium model on Mathematica 10 but the output I get is just a blank "{}". I would welcome any feedback on whether I am doing something wrong. At the moment its just ...
-2
votes
1answer
41 views

Generic approaches for multivariable polynomials across different domains [closed]

Mathematica newbie here. So I don't have a lot of time to read through the whole library of functions and language rules. So I'm trying to settle in on generic ways of doing the math that I'm going to ...
4
votes
2answers
261 views

Can I solve a certain equation?

Neither Mathematica nor Wolfram|Alpha can resolve the following. How else can I reach a solution? Reduce[(1 + x)^(2/m) - (1 - x)^(2/m) == (1 - x^2)^(1/m), x]
2
votes
2answers
129 views

Plotting the solution of a cubic equation against a coefficient in the equation

I have to plot the solution of the following equation against the coefficient $L$. Since it's a cubic equation, I'd like to filter out the real solution first and plot that then. The equation is $L ...
0
votes
1answer
84 views

Many NSolves to interpolating function

I have an expression of the form: expr = TerribleNumericalFunction[U[p]] == SimpleFunction[p] The Simple function is a ...
0
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1answer
101 views

NDSolve issue with initial and boundary conditions

While solving the heat equation in one spatial variable $u_t = u_{xx} $ (x goes from 0 to L) with the initial temperature distribution $T_0 \frac{x(L-x)}{L^2}$ , and with neumann boundary conditions ...
2
votes
1answer
62 views

How to solve an equation given certain parameters?

I am new to Mathematica so please bear with me. I have an equation that has around 7 parameters and one unknown. I was able to use FindRoot to solve it; however, I ...
4
votes
2answers
81 views

Plotting results from Findroot

I know this has been asked, but I cannot seem to understand the solutions. What I need to know, because I have my first domiciliary test this Monday, is how to plot the output from ...
6
votes
2answers
128 views

NSolve erroneously gives no solution to a polynomial system

I have a polynomial system with three equations in three unknowns, the maximum degree is 26. Two equations are symmetric, i.e. eq1(x,y,z)=eq2(y,x,z). If I search ...
0
votes
1answer
70 views

Find all degenerate eigenvalues of a cubic equation

I have an equation that is cubic in w. The three solutions correspond to bands in a bandstructure, and are a function of wavevector ...
5
votes
3answers
184 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. ...
0
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1answer
64 views

NSolve or Reduce for obtaining the results and connecting roots

Here I have one problem how to solve numerically equation for different values of one parameter x. I used just two digits because of length, but for x=0.57 I should have one real root and for others ...
5
votes
2answers
156 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 ...
1
vote
1answer
84 views

solving system of non-homogeneous advection equation using mathematica?

This question is followed up from this question How to solve a certain coupled first order PDE system Here I consider the non-homogeneous advection system \begin{equation} ...
1
vote
1answer
93 views

How to solve a certain coupled first order PDE system

I would like to find the solution $(U,V)\equiv (U(x,t),V(x,t))$ of the following system. \begin{equation} \displaystyle\left\{\begin{array}{l} \frac{\partial U}{\partial t}+(a+b x)\frac{\partial ...
5
votes
2answers
256 views
15
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2answers
1k views

How do I split up a curve into chords of equal length?

I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg. I've created ...
5
votes
2answers
458 views

Finding Points of Tangency of a Circle and a Parametric Curve

I have the following Parametric plot Generated from the following: ...
1
vote
1answer
80 views

cross point of intersecting lines [duplicate]

What is the easiest way to find the crossing point of two intersecting lines passing lets say through points line1 = {p1,p2}, line2 = {p3,p4}?