Tagged Questions

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

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0
votes
1answer
297 views

Solve telling me all my solutions are zero

I'm trying to use Mathematica to solve a complicated system of equations. Here is a screenshot of the equations, and what Mathematica outputs. The variables $v_i$ and $w_i$ act as constants in ...
10
votes
4answers
3k views

Why does Mathematica struggle with solving this equation?

Consider the evaluation of the following expression In[20]:= Reduce[ 1000 * 1.0609^t == 1500, t] ...
-1
votes
1answer
135 views

Solving an equation for asymptotic dependence of the solution on a coefficient

I have an equation I want to solve, so I entered the following into Mathematica. (x^(17/6))/(a^(17/6)) - (x^2)/a -1 == 0 where I assume $a>>1$ and $x$ is ...
3
votes
2answers
241 views

Eliminate several variables between five Conic_section equations

I want to eliminate x1, x2, y1, y2 between these 5 equations. I tried ...
2
votes
2answers
481 views

Solving set of non-linear simultaneous equations gives PolynomialGCD::lgrexp error - what next?

I'm trying to solve a set of six simultaneous non-linear equations to get a numerical answer using NSolve: ...
1
vote
1answer
213 views

Create set of equations by replacing constant values

Say I have an equation: eq = ax + by + c == 0 and I want to run NSolve on a set of equations of this form, for example: ...
3
votes
2answers
860 views

How can I solve an equation with symbolic coefficients?

I want to try to solve the following a x^(17/6) - b x^2 - 1 == 0 where a and b are ...
2
votes
2answers
261 views

Why can't FindInstance find a solution to this equation?

FindInstance[680 == 1/3 2^m (-1 + 4^v), {m, v}, Integers] FindInstance seems to be unable to find the integer solution $ {m = ...
2
votes
0answers
201 views

Am I entering this 2-variable recurrence correctly?

I'm trying to solve this recurrence with two variables. ...
1
vote
1answer
505 views

Graph and manipulate DSolve result

Given a DSolve example: ...
2
votes
3answers
785 views

Using DSolve to solve for x[t,parameter]

I'm trying to solve an ODE with two independent variables (a cannon firing from a cliff incorporating wind resistance dependent on velocity). I've tried the following for the x-component: ...
1
vote
2answers
940 views

Solving cubic equation for real roots

I'm looking to solve the following cubic equation for x: $\beta\, x^3 - \gamma \,x = c$. I have plugged in some sample values ($\beta = 2$, $\gamma = 5$ and $c = 2$). When I try to solve this ...
8
votes
3answers
526 views

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] : ...
3
votes
1answer
173 views

How can I get the general term of this recurrence equations?

Following is the recurrence relation: a[1] = 1; a[n_] := a[n - a[n - 1]] + 1 Array[a, 28] I tried to use RSolve, but it ...
0
votes
1answer
565 views

Why does Mathematica fail to solve my equation?

I am trying to solve an equation using Mathematica, but I keep getting the following error Solve::nsmet: This system cannot be solved with the methods available to Solve. More importantly, ...
16
votes
4answers
7k views

Finding unit tangent, normal, and binormal vectors for a given r(t)

For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$. I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
1
vote
1answer
189 views

Finding parameters for first positive root of solution to differential equation to be equal to a desired value

I have a differential equation with parameters. The objective is to vary the parameters such that the first positive root of the solution is equal to a desired value ...
1
vote
2answers
244 views

Is there a better way to get the eight points of intersection?

I want to get the eight points of intersection from the equations 2 Abs[x] + Abs[y] == 1 and Abs[x] + 2 Abs[y] == 1. To solve ...
0
votes
1answer
301 views

I can't get Compile to work

I've got some problems with my code, and I try to make it faster. Some of you suggested me to split my problem, and I'm here... I post the same function with and without Compile. This is a support ...
4
votes
2answers
227 views

How can I eliminate equivalent equations from a list?

I want to find the numbers $a$, $b$, $c$, $d$ of the plane $ax + by +cz +d = 0$ which make the distance from the point $M(1,2,3)$ to the plane equal to 2. I tried ...
3
votes
1answer
1k views

NSolve: Mathematica 9 issue

In Mathematica 8 the following expression evaluates and returns a result in terms of InverseFunction: ...
2
votes
2answers
320 views

How do I get the solutions of a cubic equation in trigonometric form?

I know $x^3-3 x+1=0$ has three roots that can be expressed in trigonometric form: $\{2\sin(10^\circ),\,-2\cos(20^\circ),\,2\cos(40^\circ)\}$. How can I get this result with Mathematica?
2
votes
1answer
2k views

Forcing FindRoot to return only real solutions

FindRoot documentation reports that if the equation and the initial point are reals, the solutions are searched in the real domain. However, in the following case I ...
2
votes
1answer
436 views

How can I solve an exponential inequality in Mathematica?

I would like to solve the equation: A Exp[m t + s Sqrt[t] x - 1/2 s^2 t] >= K with respect to x (which is in the exponent) ...
2
votes
1answer
133 views

What's the difference between the following two codes?

I have two codes to find the integer numbers $m$, $x$, $y$, $z$ in the system of equations. First code ...
4
votes
2answers
815 views

Can mathematica solve this equation?

I have the following Mathematica code to solve an equation coming from isoparameteric finite element for quadratic tetrahedron element. I need to get the iteroplation fast and accurate. I only find ...
0
votes
1answer
171 views

Manipulate[]'ing complex roots of an equation using a 2D slider [closed]

I want to make a demonstration of how the complex roots of a polynomial change when I alter the coefficients. Here is my attempt: ...
8
votes
2answers
693 views

How to solve a system of equations of the Vietnamese Mathematical Olympiad?

This is a system of equations of the Vietnamese Mathematical Olympiad 2013, the first day. Solve the system of equations $$\begin{cases} \sqrt{\sin^2 x + \dfrac{1}{\sin^2 x}} + \sqrt{\cos^2 y + ...
2
votes
1answer
139 views

Using NSolve on an equation that involves Mean and TruncatedDistribution

What I would like to do is create a mixture distribution that has a specified mean by varying one parameter in the distribution. To do this I've written the following code; ...
4
votes
0answers
112 views

Symbolic solution to ODE, pure InverseFunction not evaluated

I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
6
votes
1answer
604 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}] ...
0
votes
0answers
29 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: ...
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 ...
4
votes
1answer
504 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. ...
46
votes
2answers
4k 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
votes
1answer
800 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
votes
1answer
1k 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 ...
8
votes
2answers
524 views

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 ...
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 ...
0
votes
1answer
242 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 ...
12
votes
6answers
2k 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?
8
votes
3answers
2k views

First positive root

Simple question but problem with NSolve. I need help how to extract first positive root? For example: ...
2
votes
0answers
268 views

FindRoot - Speed and errors

I am using FindRoot[] to solve a complicated equation. It seems I get the correct answer even though I get errors about an ...
11
votes
3answers
3k 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 ...
3
votes
3answers
684 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
votes
0answers
97 views

Why cant Mathematica solve this equation? [duplicate]

Possible Duplicate: Can Reduce *really* not solve for x here? Why cant Mathematica solve this equation? ...
1
vote
1answer
376 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
votes
1answer
211 views

How to solve this trigonometric system of equations numerically?

How can the following trigonometric system of equations be solved numerically? ...
0
votes
1answer
218 views

Solve not satisfying simple boundary conditions

I am trying to solve the following equations for the coefficients c1 and c2. ...
2
votes
0answers
393 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, ...