Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
0
votes
1answer
94 views
ContourPlot of a complicated function
I have the function $pot_1(x,y,z)$ which is given in analytical form. So, in order to plot the contours at the primary planes $(x,y)$, $(x,z)$ and $(y,z)$, I use the following ...
2
votes
1answer
141 views
Solving an equation involving a determinant
I have a matrix which doesn't include numerical values. There are four variables in it. It is defined by
...
-3
votes
1answer
194 views
Why can't Mathematica solve these non-linear equations? [closed]
$l_{2}$ and $\theta$ are the variables. All other parameters are constants. I need to find $l_{2}$ and $\theta$ in terms of these constants.
$\frac{\mu_{0}\sin(\theta-\theta_{0})}{\sqrt{l_{2}^2 ...
1
vote
0answers
70 views
Solving for vector elements in a function to which the vectors are not passed explicitly
I want to define a function which takes in two integers (indicating the lengths of 2 vectors), and solves a simple set of expressions at a set of points to find all the values in both the vectors.
so ...
4
votes
1answer
141 views
Can mathematica resolve this equation?
Obviously，the equation $x^2-3 y^2=2 z^2$ doesn't have positive integer solutions.
I tried
...
3
votes
1answer
88 views
How can I get a single solution to a set of inequality constraints?
I have a set of constraints to which I require integer solutions. However, instead of needing all possible integer solutions (as obtained by using ...
4
votes
2answers
209 views
All possible solutions to the Matrix Equation (free variables appearing)
I am attempting to solve a system of linear equations using LinearSolve[] . In my case, the number of unknowns are more than constraints. I learnt that LinearSolve ...
1
vote
1answer
130 views
Stop Mathematica from giving imaginary solutions
I have the following equation:
$$D=\frac{1}{64} \pi A ^3 B \sin \left(C\right)-\frac{1}{2} \pi A B \sin \left(C\right)$$
which I want to solve for $A$. The equation is cubic in $A$ so this should ...
1
vote
1answer
100 views
2
votes
1answer
154 views
How to solve equations self-consistently
I want to solve the following equation self-consistently. So,
H.u = e.u
{{1, d}, {d, 1}}.{u1, u2} = e.{u1, u2}
I guess an initial value for ...
1
vote
1answer
124 views
How can I get the solution of complicated implicit function?
The question is what is the method to solve the implicit function has real and imaginary number.
For example, The function is F(x,y)=(-I*x + 2*y^2)^2 + x^2 - 4*y^4*Sqrt[1 - I*x/(y^2)].
Although I ...
0
votes
1answer
70 views
Evaluating derivatives for use in solve
I need to evaluate the derivative of a function. My function looks like
approx[vector_, x_] := Sum[vector[[n]]*Basis[n - 1, x], {n, 1, Length[vector]}]
and I'm ...
4
votes
2answers
137 views
Finding all/most roots of a discontinuous function more consistently?
I have the equation:
f[x_]:=α Tan[α*a] - Sqrt[c - α^2]
and ideally I want to find all of its positive zeros, given a and c, with variable alpha. The problem is ...
1
vote
0answers
121 views
NDSolve equations contain solution from solving cubic equations
I'm having trouble using NDSolve to solve equations that were obtained from solving cubic equations.
In my problem, I first obtained 6 functions (ca1, ...
2
votes
1answer
93 views
How to transform an expression using algebraical instead of pattern rules [duplicate]
I would like to transform rules algebraically. A very simple example would be: -
k^2 - 2 k x + x^2 /. {2*k -> 1}
This transforms to: -
$$k^2-2 k x+x^2$$
...
1
vote
0answers
91 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
90 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
323 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:
...
7
votes
2answers
227 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, ...
2
votes
3answers
235 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
245 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
147 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
112 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
94 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 $m$
...
14
votes
1answer
413 views
Bug in Solve (Mathematica 9)
Just came across the strangest bug under both Mathematica 9.0.0 and 9.0.1. If one enters:
Solve[m == p Sin[x] && -Pi/2 < x < Pi/2, x]
... then ...
0
votes
1answer
157 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 ...
6
votes
4answers
536 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]
During evaluation of In[20]:= Reduce::ratnz: Reduce was unable ...
-1
votes
1answer
99 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
152 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
198 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:
...
0
votes
1answer
54 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:
...
0
votes
0answers
93 views
using FindRoot in for loop [closed]
I am fairly new to Mathematica so I am not really familiar with all the "kinks" in its syntax (a matlab lover).
I am trying to run this:
...
3
votes
2answers
173 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
83 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
106 views
Am I entering this 2-variable recurrence correctly?
I'm trying to solve this recurrence with two variables.
...
0
votes
1answer
121 views
2
votes
3answers
258 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:
...
0
votes
3answers
438 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 ...
7
votes
3answers
252 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] :
...
2
votes
1answer
107 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
0answers
181 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, ...
7
votes
3answers
853 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
96 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
129 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
163 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
133 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
...
2
votes
1answer
398 views
NSolve: Mathematica 9 issue
In Mathematica 8 the following expression evaluates and returns a result in terms of InverseFunction:
...
2
votes
2answers
195 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?
1
vote
1answer
332 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 ...
0
votes
0answers
186 views
Vertices of the region defined by inequalities
I have a set of 8 inequalities in two variables $X$ and $Y$. In Mathematica, using the command Reduce I find the solution. The solution plotted with ...
