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

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1answer
1k 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 ...
2
votes
1answer
1k 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
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2answers
110 views

Puzzling behavior produced by Exists

I need to simplify a set of solutions of a system, say for example: ...
0
votes
1answer
263 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 ...
3
votes
1answer
2k 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 ...
0
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1answer
207 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: ...
1
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1answer
586 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 ...
13
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3answers
5k 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
1answer
165 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
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1answer
244 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
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1answer
249 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 ...
2
votes
1answer
2k 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 ...
4
votes
3answers
3k views

How to solve this system of equations?

I want to solve the following system of equations: $$\begin{cases} 1+\sqrt{2 x+y+1}=4 (2 x+y)^2+\sqrt{6 x+3 y},\\ (x+1) \sqrt{2 x^2-x+4}+8 x^2+4 x y=4. \end{cases}$$ I tried ...
1
vote
1answer
138 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 ...
1
vote
4answers
4k 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 ...
2
votes
0answers
186 views

Why is FindRoot initial value far from the specified one?

I am trying to numerically find the root of a function that looks a bit like: 1/x - (SchurDecomposition[A[x]][[2]])[[1]], where ...
7
votes
3answers
547 views

Efficient code for solve this equation

We have $a*b*c=-1$, $\frac{a^2}{c}+\frac{b}{c^2}=1$, $a^2 b+a c^2+b^2 c=t$ What's the value of $a^5 c+a b^5+b c^5$? I tried ...
2
votes
0answers
207 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 ...
14
votes
2answers
356 views

FindInstance returns Indeterminate in version 9, but not in 8

Bug introduced in 9.0 and fixed in 10.0.0 Here is a trivial system of equations in three unknowns for which FindInstance obtains a solution: ...
2
votes
2answers
376 views
0
votes
1answer
125 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}] ...
1
vote
1answer
93 views

Calibrating Precision in calculations

As the title says, I encounter an irritating problem which has to do with the accuracy or the precision used in the calculations. To be more specific, I have the following code: ...
1
vote
1answer
596 views

Forcing evaluation of ArgMax

How to force evaluation of ArgMax before its output gets used in Solve? Background: I'm trying to solve for the Nash ...
0
votes
1answer
212 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
481 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 ...
-1
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1answer
2k 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
94 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
255 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
154 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 ...
3
votes
2answers
845 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
552 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
543 views

Solve equation with inequalities for parameters

I want to solve following equation: ...
2
votes
1answer
1k 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 ...
0
votes
1answer
3k 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 ...
0
votes
1answer
263 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
736 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 ...
2
votes
1answer
151 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
293 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 ...
4
votes
2answers
161 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
680 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
479 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
536 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
1k 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
272 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 ...
2
votes
2answers
335 views

Get the approximate analytical solution to an algebra equation

Is there a way to get the analytical form to the root of this equation: 2 A e (-ArcTanh[smax/s0] + ArcTanh[(smax Cos[w ζ])/s0]) == F0 ...
0
votes
1answer
311 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
144 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
836 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
425 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
5k 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] ...