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Questions tagged [equation-solving]

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

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57 views

Handling “Solve was unable to solve the system with inexact coefficient” errors [duplicate]

Possible Duplicate: How to get rid of warnings when using Solve on an equation with inexact coefficients? I've been trying to calculate the following in Mathematica: ...
15
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5answers
3k 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 ...
4
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1answer
1k views

How do I use RSolve to solve a system of recurrence relations?

I am trying to solve a system of recurrence relations as follows. ...
90
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2answers
20k views

What is the difference between Reduce and Solve?

Solve and Reduce both can be used for solving equations. Just by working with them, I know there are some differences between ...
3
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1answer
1k views

Solve pair of recurrence relations

[Corrected equations and added simple example] Can you solve a system of (loosely) coupled recurrence relations like this in Mathematica somehow? ...
3
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1answer
3k views

Solving an Integral equation

I would like to solve the equation $$\frac{2}{p}\int_0^1((1-u)^{1-p}+u^{1-p})^{\frac{1}{p}}\text{d}u=42$$ for p numerically. I tried ...
13
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2answers
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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 <...
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4answers
3k 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 ...
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1answer
469 views

How to express endogenous variables in terms of exogenous variables?

I have 11 endogenous variables (RD, NR, WR, Q, NQ, R, L, W, NU, C1, C2) and two exogenous variables (EE, K). I'm trying to find $RD = f(EE, K),\, NR = f(EE, K),\, ...,\, C2 = f(EE, K)$. Hence, I ...
14
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6answers
6k views

How to find lattice points on a line segment?

How do I find points on the line segment joining {-4, 11} and {16, -1} whose coordinates are positive integers?
11
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3answers
7k views

First positive root

Simple question but problem with NSolve. I need help how to extract first positive root? For example: ...
21
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4answers
9k views

Find all roots of an interpolating function (solution to a differential equation)

I'm trying to find all the roots of the solution to a differential equation. Using NSolve or Reduce I don't get the roots, so I'm using an iterative method which I found in physicsforums.com. This ...
4
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3answers
2k views

Solving Integrals

Here's a problem that I don't understand. f[x_] := Exp[Cos[3*x]] g[x_] := (1/3)*x^3 - x^2 + 2 When I try to find the limit: ...
2
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0answers
135 views

Why can't Mathematica solve this equation? [duplicate]

Possible Duplicate: Can Reduce *really* not solve for x here? Why can't Mathematica solve this equation? ...
2
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1answer
2k views

How to extract Solve results as variables [duplicate]

Possible Duplicate: Assign the results from a Solve to variable(s) In the following example: ...
4
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1answer
462 views

How to solve this trigonometric system of equations numerically?

How can the following trigonometric system of equations be solved numerically? ...
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1answer
280 views

Solve not satisfying simple boundary conditions

I am trying to solve the following equations for the coefficients c1 and c2. ...
2
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0answers
664 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, ...
7
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1answer
944 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
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1answer
981 views

Find asymptotics of a function

Can Mathematica find the asymptotics of a function in the following sense? I have Log[1/n^2]/Log[4^(-Sqrt[Log[n]]) + (2^(-Sqrt[Log[n]]) - 1)^2] and I would like ...
1
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1answer
95 views

How to get a solution involving logs in the right form?

How do I get Solve[(1/9)^(r/2) == 1/n , r] to give me Log[n]/Log[3] and not ...
10
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2answers
1k views

Solving/Reducing equations in $\mathbb{Z}/p\mathbb{Z}$

I was trying to find all the numbers $n$ for which $2^n=n\mod 10^k$ using Mathematica. My first try: Reduce[2^n == n, n, Modulus -> 100] However, I receive ...
5
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2answers
358 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 ...
3
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1answer
1k 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: ...
4
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1answer
422 views

Eliminating functions from system of PDE in Mathematica

Mathematica users, Let's see an example of three PDEs: How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
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2answers
375 views

How to use Solve rules as a function body?

Solve gives me an expression which I want to use as the body of a function. Rather than run Solve every time inside my function ...
2
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2answers
661 views

How to express Polynomial in a certain format with Mathematica?

Equations ...
2
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1answer
224 views

Remove failed Solve[] attempts

I can't figure how to replace a failed evaluation with a null value. I am very new to Mathematica. I have an equation that are being processed using the Solve[] ...
7
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3answers
729 views

NDSolve and {C, K, Slot} and other built-ins as a variable name

The following problem is an exploration of what causes the error "Input is not an ordinary differential equation" in Mathematica as it seems to have changed from version 8 to version 9. Specifically ...
3
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3answers
1k views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
14
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2answers
638 views

Is there a way to use functions like Prime[n] within Solve[]?

I'm trying to see if a number can be written as the sum of two prime numbers. Ideally, I would like to use Solve[ Prime[n] + Prime[m] == 100, {n, m}] But that ...
3
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0answers
204 views

RSolve not returning known solution

I have the following recurrence relationship for which I know the solution is given by a binomial distribution: ...
1
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1answer
228 views

Solving a large equation set

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1answer
167 views

Industrial Level Applications. Recipe for mixed notation of equations set

I am working with large (linear) equations set within Mathematica in numerical notation. For example, set from 4056 eq. is solved for a second, no more. There is no doubt, result is great. But even ...
2
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1answer
1k 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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3answers
3k views

Tricks for solving (lots of) coupled nonlinear equations numerically?

I have a system of 6 non-linear (quadratic) coupled equations with 6 complex unknowns \begin{align*} |x_1|^2 + |x_2|^2 + |x_3|^2 &= a\\ x_1 x_4^* + x_3 x_5^* &= b + c i\\ x_1 x_6^*...
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1answer
1k views

Assign the result of Solve in a list [duplicate]

Possible Duplicate: Assign the results from a Solve to variable(s) I want to assign the results of a Solve command in a list. For example Solve[-((287 s^3)/50) == 0, s] returns {{s -> 0}, {s -> 0}...
3
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1answer
755 views

How to modify a matrix to satisfy a special condition?

I have matrix like this: How do I modify this matrix to make it satisfy the following condition: For each element {i, j} in the matrix the sum of the elements of row i must be equal to the sum of ...
9
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5answers
985 views

Create filling between two trig functions

Working with trig functions, period, amplitude, etc. I found a worksheet at a calculus website, with some nice questions related to interpreting trig functions, at least, they provide some "fun" ...
18
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2answers
967 views

Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, <...
11
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3answers
4k 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 ...
4
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1answer
727 views

Both Sin[x]==0 && Cos[x]==0 as a solution

If I do FullSimplify[Reduce[Sin[p1] == 0 && Cos[p1] == 0, Reals]] I get Cos[p1] == 0 && Sin[p1] == 0 ...
2
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2answers
1k views

FindRoot errors

I'm trying to solve a system of two equations in two variables for some range of parameter values. I use ContourPlot to see where I should look for a solutions and ...
0
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2answers
227 views

Derivative of the solutions by parameter

P0 = 0.1; K = 1000; Quiet[sol = Solve[{K*P*L == PL, P0 == P + PL, r*P0 == L + PL}, {P, L,PL}][[1]]]; complex = PL /. sol; Plot[complex, {r, 0.1, 2}] How can I ...
6
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2answers
2k views

Solve an equation in $\mathbb{R}^+$

How can I solve this equation (both numerically and literally) only in the positive reals $\mathbb{R}^+$? Solve[x == (v0 - (A CD t v0^2 ρ)/(4m)) Cos[θ] t, t] And ...
0
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1answer
361 views

x/.NSolve[f==g,x] does not work when f or g is the output of NDSolve!

I have been trying to put Points at the intersection of two curves, one of which is the ouput of a differential equation solved with NDSolve. The output being an Interpolation, NSolve cannot find the ...
3
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1answer
2k views

How to solve this equation with positive integers as a solutions?

This is a problem of United Kingdom Mathematical Olympiad. Find all triples $(x,y,z)$ of positive integers such that $$\biggl(1+\dfrac{1}{x}\biggr)\cdot \biggl(1+\dfrac{1}{y}\biggr)\cdot \biggl(1+\...
15
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3answers
2k views

NSolve gives additional solutions that don't satisfy the equations!

I am trying to solve the following polynomial equations in Mathematica: ...
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1answer
359 views

How to find 4 unknowns?

There are 4 unknowns constants: a,b,c,p. The variable is ...