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

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1
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0answers
270 views

Automatic inverse for Lambert’s Azimuthal Equal-Area Projection

I’m interested in finding closed-form inverses for map projection equations in general (of course, this is not always possible). I’m hoping Mathematica can help me with some of the trickier ones. As ...
3
votes
2answers
145 views

Find condition under which variables fall away

I have a somewhat lengthy expression, looking like expr = 1 + x + b + Pi + 2*a Is there some way of generating a relationship between ...
4
votes
2answers
608 views

How do I solve N simultaneous equations for N variables?

I have a function: f[x_] := x + 31 x^3 + 5 x^25 Which I want to find an expansion for: ...
8
votes
2answers
442 views

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, ...
4
votes
3answers
494 views

Symbolic derivative of $n$-term product

I want to determine the relationship that must exist between the $x_i$ and $y_i$ such that $$ \frac{\partial}{\partial\theta} \prod_{i=1}^n \frac{f(x_i,\theta)}{f(y_i,\theta)} = 0, $$ where $$ ...
8
votes
2answers
957 views

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 ...
3
votes
1answer
259 views

What properties make this equation difficult to symbolically solve?

I tried to solve the following equation with Mathematica's solve: Solve[K*(2*Tan[L/2*Sqrt[P/(EI)]]-L*Sqrt[P/(EI)])+4*P*Sqrt[P/(EI)] == 0, P] It gave the ...
0
votes
1answer
286 views

Reap and Sow From NDSolve solution

I want to get the answer of my NDSolve in the form of table (the value of each x and y). ...
0
votes
2answers
143 views

How to get special solutions of this system of equations?

I only want to get all the solutions of this system of the solutions with a value of $k$, we have the same values ​​of $m$ ...
21
votes
1answer
810 views

Bug in Solve (Mathematica 9)

The issue seems to be fixed as of Version 10.1. Just came across the strangest bug under both Mathematica 9.0.0 and 9.0.1. If one enters: ...
0
votes
1answer
374 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 ...
11
votes
4answers
4k 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
154 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
252 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
632 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
287 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
1k 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
344 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
241 views

Am I entering this 2-variable recurrence correctly?

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

Graph and manipulate DSolve result

Given a DSolve example: ...
3
votes
3answers
1k 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: ...
2
votes
2answers
1k 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
632 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
235 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
734 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, ...
17
votes
4answers
9k 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
255 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
280 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
365 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
280 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 ...
4
votes
1answer
2k views

NSolve: Mathematica 9 issue

Bug introduced in 9.0 and fixed in 10.0.0 In Mathematica 8 the following expression evaluates and returns a result in terms of InverseFunction: ...
2
votes
2answers
447 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
3k 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
517 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
135 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
1k 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
192 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: ...
9
votes
2answers
875 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
149 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
120 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
784 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
34 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: ...
10
votes
5answers
2k 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
625 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. ...
54
votes
2answers
6k 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
956 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
2k 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
648 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
2k 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
274 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 ...