Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
0
votes
1answer
90 views
How to guess initial complex value for FindRoot
I have to solve a transcendental equation for a parameter, say $\beta$. Now, the $\beta$ has a range from $ik$ to $k$ where $i$ is the usual imaginary root $\sqrt{-1}$ and $k$ is a real number. ...
0
votes
1answer
74 views
1
vote
0answers
49 views
Finding Maximum Root [duplicate]
How can I find the greatest root for a polynomial if the polynomial degree is very large.
One way is using NSolve. This command can find all roots in numeric. Then, ...
5
votes
1answer
93 views
Find the domain in which a sequence converges
I seem to have a lot of problems in the format of:
Given the sequence $a_n=\frac{n^\alpha+1}{2n^8+5}$, for $\alpha > 0$, find the values of $\alpha$ such that the sequence converges.
However, ...
0
votes
0answers
110 views
How to find the couple $a$ and $b$ of the equation? [closed]
I want to find the integers numbers $a$, $b$, $k$ of the equation
Sqrt[2 x + a] + Sqrt[b - 2 x] == k
so that the given equation has two reals solution.
I ...
7
votes
2answers
232 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, ...
1
vote
3answers
199 views
0
votes
2answers
74 views
Reduce on equations involving integrals
Here's part of problem from a college physics text:
A time-dependent force F = (8.00 i - 4.00 t j) N (where t is in
seconds) is applied to a 2.00-kg object initially at rest. (a) At what
time ...
0
votes
3answers
76 views
Help solving a system [closed]
I am trying to solve this system for r and c but I get an error "Solve::ivar: r is not a valid variable.".
What is wrong here?
...
2
votes
0answers
94 views
differential equations with implicit functions
I have an ordinary differential equation that contains coefficient functions that depend implicitly on the independent variable via an algebraic equation. I am trying to go ahead and use NSolve to ...
2
votes
1answer
80 views
InterpolatingFunction with growing Domain
I want to find roots of a function that is very slow to calculate (the function itself involves a bunch of FindMaxima) so I interpolate the function in a region where I think it likely the the root ...
1
vote
1answer
145 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[] ...
2
votes
1answer
114 views
Computing the sign of the real part of eigenvalues in a 3D linearized system with 3 parameters
So I have this dynamical system given by:
$$
\left\{\begin{aligned}
x' &= a(y-\phi(x))\\
y' &= x-y+z\\
z' &= -by
\end{aligned}\right.
$$
where $\phi(x) = \mu x^3 - \nu x$ and $a,b,\mu,\nu$ ...
2
votes
2answers
127 views
A While Loop with two different steps/iteration
I'd like to know if there is a possibility to solve an equation in a while loop with 2 different steps. I want the step to be small at the beginning and bigger after a certain value of sigma (sigma is ...
3
votes
2answers
141 views
2
votes
2answers
65 views
How do I generate a set of n-tuples containing integral solutions to a linear equation provided certain constraints?
Let $m,k,p$ be fixed positive integers. I want to create a table of k-tuples $(x_1,x_2,\ldots,x_k)$ comprised of solutions in positive integers to the equation below:
...
2
votes
1answer
207 views
NDSolve two PDE plus one ODE, together
I have a couple of PDE (time and space/length) that are correctly managed by NDSolve, but to which I’m adding an ODE on which the acc “accumulates”, through time, a ...
2
votes
1answer
61 views
Differentiating with respect to vectors of unspecified length
Given a function defined by
f[x_,y_] := Sum[ x[[i]] (g[y[[i]]] - g[Total[y]] - Log[x[[i]]]), {i, 1, Length[x]}]
I can easily calculate the derivative for a fixed ...
1
vote
2answers
88 views
Rearranging an equation with the sine function in it [closed]
When I evaluate Solve[a==Sin[b*c], b] to rearrange the following for $ b $:
$$ a = \sin(bc) $$
I get the following result from Mathematica:
$$\begin{align*} ...
4
votes
2answers
87 views
Extracting Reduce results
I'm solving a Diophantine equation inside of a function using Reduce but I'm having trouble extracting the necessary parts of the answer.
For example, if my input ...
0
votes
1answer
275 views
Solving derivative of cumulative normal distribution log likelihood
I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of ...
3
votes
1answer
460 views
Solve pair of recurrence relations
[Corrected equations and added simple example]
Can you solve a system of (loosely) coupled recurrence relations like this in Mathematica somehow?
...
7
votes
3answers
303 views
NDSolve and {C, K, Slot} and other built-ins as a variable name
The following problem is an exploration of what causes the error "Input is not an ordinary differential equation" in Mathematica as it seems to have changed from version 8 to version 9.
Specifically ...
4
votes
1answer
230 views
NDSolve does not respond
For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
9
votes
2answers
630 views
Solving a time-dependent Schroedinger equation
I want to solve the time-dependent Schroedinger equation:
$$
i\partial_t \psi(t) = H(t)\psi(t)
$$
for matrix, time-dependent $H(t)$ and vector $\psi$.
What is an efficient way of doing this so ...
2
votes
2answers
92 views
Puzzling behavior produced by Exists
I need to simplify a set of solutions of a system, say for example:
...
0
votes
1answer
242 views
DSolve fails to solve second order PDE
I have a very simple example of a second order PDE:
eqn = D[u[x, y], x, y] + u[x, y] == 0;
sol = DSolve[eqn, u, {x, y}]
and Mathematica cannot solve it! What is ...
0
votes
1answer
124 views
Dynamic boundaries for FindRoot
As documented
FindRoot[f[x], {x, xs, min, max}]
searches for a solution, stopping the search if x ever gets outside the ...
4
votes
2answers
337 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
3answers
1k 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 ...
0
votes
1answer
106 views
Solving a differential equation for a variable in a function
This may sound like a very trivial question, but I need to solve a differential equation as follows:
...
0
votes
0answers
45 views
Solving ODEs produces error NDSolve::nrnum1
I'm a new member but I have been reading the great answers here for sometime now.
I am trying to solve a system of ODEs for various values of a parameter epsilon, using a slider. I am using ...
1
vote
1answer
101 views
Substituting solution from Solve into the equation and making a plot
I want to solve an equation and substitute it into a Plot expression. My code looks something like this
a[b_, x_] := bx + 1;
sol = Solve[(1 + b)x + 1 == 0, b]
I ...
2
votes
1answer
99 views
Any solution to system of equations?
I need ANY combination of 8 variables which satisfy:
a+b+c+d+e+f+g+h=0
a^2+b^2+c^2+d^2+e^2+f^2+g^2+h^2=1
a*b+b*c+c*d+d*e+e*f+f*g+g*h+a*h>2/3
Ideally these ...
7
votes
1answer
100 views
How to plot inequalities taking into account that points must be integers and not reals?
I have solved with Mathematica 9 the following integer inequalities using Reduce:
...
1
vote
1answer
151 views
Is my system too complicated for Solve?
I am trying to solve a system of three nonlinear equations using Mathematica. Solve takes forever to run and never solves my system of equations. Is my system too ...
0
votes
1answer
119 views
How to solve a simple inequality
I am having trouble getting Mathematica to solve really simple inequalities.
I started with
Solve[{y^x >= 2*y - 1}, x]
but Mathematica can't solve it. So I ...
0
votes
3answers
271 views
How can I use assumptions with FindRoot?
I have something like
FindRoot[f[x], {x, a}]
Now I want FindRoot to constrain the solutions to 0 < x < 1. How can I ...
1
vote
1answer
80 views
Why Solve and Simplify give different results? [closed]
I want to solve the following equation
y == (1/(1/4 + y) - 1/(3/4 - y))/((1/4 + y) + 1/(3/4 - y))
I tried
...
0
votes
0answers
91 views
“Nesting” FindInstance and FindRoot
The problem I face involves three constrained optimization problems (which i will call B,R and F) which interact. The optimization problem F is solved "after" (in terms of the model behind the ...
0
votes
1answer
141 views
3
votes
3answers
215 views
Efficient code for solve this equation
We have know $a*b*c=-1$, $\frac{a^2}{c}+\frac{b}{c^2}=1$, $a^2 b+a c^2+b^2 c=t$,
What's the value of $a^5 c+a b^5+b c^5$?
I tried
...
1
vote
1answer
83 views
Finding rational roots to an equation (univariate) [closed]
So I'm using Mathematica 7 for Students and I'm using the Root function to find the roots of an equation over the rational numbers:
$$225x^6 -343 = 0$$
I created ...
8
votes
2answers
445 views
How to solve a system of equations of the Vietnamese Mathematical Olympiad?
This is a system of equations of the Vietnamese Mathematical Olympiad 2013, the first day. Solve the system of equations
$$\begin{cases}
\sqrt{\sin^2 x + \dfrac{1}{\sin^2 x}} + \sqrt{\cos^2 y + ...
2
votes
0answers
139 views
Solving $k\log(n) - k\log(k) \leq u$
How can I persuade Mathematica to help me find solutions to the inequality
$k\ln(n) - k\ln(k) \leq u$ over the reals, assuming $u \geq n \geq k \geq 1$.
When I evaluate
...
10
votes
1answer
118 views
FindInstance returns Indeterminate in version 9, but not in 8
Here is a trivial system of equations in three unknowns for which FindInstance obtains a solution:
...
2
votes
2answers
99 views
Defining a function by pieces using list of interpolated functions in order to use `FindRoot`
I have two lists with the interpolated functions
...
6
votes
2answers
1k views
How can I get Mathematica to solve an equation with multiple variables?
How can I get mathematica to solve the non-homogeneous differential equation with undetermined coefficients listed below?
Solve $\ y''(t)+3y'(t) = 2t^4 $, using: $\ y_p(t) = ...
0
votes
1answer
62 views
Collecting roots of different equations and create a list
I solve two equations and have two solutions one by each equation. I want to create list of these roots. Could anyone please help me? Appreciate it.
m02R150 = FindRoot[P1 == 0, {E1, 0.07, 0.1}]
...
3
votes
1answer
92 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 ...
