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

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0answers
1k views

Solve[] unexpectedly giving empty solution sets for extremely large problems

I was calculating the set of lattice vectors in $\mathbb{Z}^4$ which have taxicab norm $r$. For example, executing ...
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1answer
158 views

I got wrong answers when solving an equation

I have this expression: ...
3
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1answer
210 views

Faster Solve for Fermat 4n+1 conjecture

Assuming that Fermat 4n+1 conjecture (each prime of the form 4n+1 is the sum of two squares) is true then I like to solve the ...
2
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1answer
146 views

Decomposing a diagonal positive real matrix

I would like to 'decompose' a diagonal positive real matrix $E$ of rank $D$ onto $\sum_{i=1}^{D}c(i)N^i$: $$E = \left( \begin{array}{ccc} 0 & & & \\ & a & & \\ ...
0
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1answer
287 views

How to enter and solve this equation in finite fields?

Is there a way in Mathematica 9 to enter and solve the following equation $p(x) = r^x$ where $p(x)$ is a polynomial whose coefficients are drawn from a finite field, and $r$ is a primitive root of ...
2
votes
2answers
192 views

Quadratic Equations $\bmod p^k$

As part of a larger program, I need to solve $A x^2+B x+C \equiv 0 \pmod {p^k}$ for prime $p$. Right now I'm doing this by calling ...
1
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0answers
329 views

No response from DSolve

Using optimal control theory, I am trying to find the optimal paths of d and k such that they will maximize profit as given by lc: ...
1
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1answer
264 views

Perform FindRoots on Function Evaluation Containing RootSearch

I am using Ted Ersek's RootSearch function in Mathematica 9.0 (http://library.wolfram.com/infocenter/Demos/4482/) to create a function that I am using for graphing. ...
3
votes
3answers
591 views

Extracting coefficients from g=a*x+b*y+c*x*y

I have a Response Surface Equation (RSE) that I'm trying to extract coefficients from. It has a form similar to: g = a*x + b*y + c*x*y; I want to be able to ...
1
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1answer
190 views

Problem to solve an integral equation [closed]

I am new to Mathematica. I am trying to numerically solve for C in the following equation: $\begin{equation} \begin{array}{lcl} -\int_0^\infty (5000000+100000 x+ C)^{-1} ...
2
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1answer
253 views

Solving Complex Equation Over Reals

I want to solve the equation $\frac{abi}{a+bi}=4-2i$, where $a$ and $b$ are real numbers. I know from hand-solving the answer is $a=5$, $b=-10$. How do I get Mathematica to tell me this? I tried: ...
2
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1answer
537 views

Resonance Curve using NDSolve

I am trying to make a resonance curve like this one below, using NDSolve. I tried to use code as below. Basically I try to hold solution for a w (driving frequency value) using NumericQ and then ...
0
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1answer
99 views

Failure message from Reduce

I am getting the message Reduce::nsmet: This system cannot be solved with the methods available to Reduce. while trying to solve the following equation: ...
5
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1answer
314 views

Calculate max value

Update Using ...
0
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0answers
43 views

Store results of inequality [duplicate]

I eveluated some values using Reduce commend and I store them in a Table ...
2
votes
1answer
200 views

Solving problems with the floor function

I've got the following problem: If I want to calculate the following equation, ...
2
votes
2answers
210 views

Plotting double inequality only for integer values

RegionPlot is plotting for all values. And using ListPlot I can only evaluate one inequality. How can I plot this type of ...
2
votes
3answers
853 views

Solve the system of equalities and inequalities

I have a system of expressions, in which each expression is an equality or inequality expression of the following form: Var = Var1 + Var2 Var $\odot$ number Var $\odot$ Var1 $\odot$ = $\leq | \geq | ...
1
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3answers
147 views

Discrete inequality plotting

I have an equation like this: $${20 \choose k}\cdot \sum_{i=0}^k {k \choose i}\cdot i \leq 1+f$$. I want to plot this inequality as the dependency between k and ...
1
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3answers
119 views

Applying Reduce[] to a table [duplicate]

I have a table for example: t = Table[k,{k,5}] which returns {1,2,3,4,5} and for every element in this table I want to check when it is $\leq 1 + a$. I ...
0
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0answers
169 views

Assigning the answer of Solve to a variable [duplicate]

If I enter Solve[(x-2)(x+2)==0,x] then the answer comes up as {{x -> 2}, {x -> -2}} I want to make two variables ...
6
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1answer
513 views

How to get vertices of a polytope given by equalities and inequalities?

I have a polytope given by some equalities and inequalities, how can I get all the vertices of the polytope? If there's a way to deal with the one given by inequalities only, how can I reduce the ...
1
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1answer
179 views

Solve returns a wrong answer

I'm afraid the following is rather localized questions, but I don't know how to simplify and generalize it. I have the following two points (in the real plane): ...
3
votes
3answers
465 views

How can I calculate a combination of limit and sum?

How can I solve the above problem? I enter it as: Limit[Sum[Sqrt[1 + i^2/n^2]/n, {i, n}], n -> Infinity] but this is not working:
1
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1answer
320 views

NSolve with numerical function

I would like to solve numerically an equation which involves a numerical function constructed by fitting some data: ...
0
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3answers
397 views

Solving a differential equation with mixed conditions using DSolve

I want to solve a differential equation $$ \frac{d}{dx}\left(k_0 \left(\frac{T(x)}{T_0}\right)^n \frac{dT(x)}{dx}\right)=0,$$ with boundary conditions: $T(l)=T_0$, $\;T'(0)=-\frac{q_0}{k_0 ...
2
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2answers
285 views

Check if integer has even number of digits

I want to check if a number has an even or odd number of digits. 10 would be even because it has 2 digits 300 would be odd ...
10
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3answers
450 views

Reduce can't reduce an equation without appropriate assumptions

When there are three unknowns (x, y, z), Mathematica can solve it: ...
4
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5answers
590 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
2
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1answer
188 views

How can I exhibit the evaluation of formulas in a Mathcad-like way?

How can I create a function F that works like this: x = 2 f1 = x^2 + 3 f2=x+5 F[f1] x^2 + 3 = 2^2 + 3 = 7 ...
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1answer
1k views
1
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0answers
456 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = ...
15
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1answer
1k views

What are the algorithm details of FindRoot?

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system". But I ...
1
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0answers
593 views

Why DSolve and NDSolve give different answer

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? Which one is ...
0
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1answer
145 views

Small problem at equation solving

I have $2$ equations in $2$ parameters which involve integrations. The limits of the integrals can not be defined analytically. They also require equation solving and eventually I couldnt incorporate ...
2
votes
1answer
116 views

Plotting the solution of a 2nd order equation

I have got to solve a second order equation, where the coefficient depend on the parameter $k$: $$(A_k - \omega) (D_k- \omega) - B_kC_k = 0$$ so that also the solution $\omega=\omega(k)$ will depend ...
2
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1answer
461 views

Solving System of Inequalities Relatively

I have been trying to figure out how to solve a system of inequalities relatively. I don't care about values, I just want all possible ordering. An example system might be:$${b > r,\; p > r,\; c ...
0
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1answer
479 views

NDSolve + FindRoot for Bessel Zeros

I am trying to use a solution given by Michael E2 in this topic: ...
1
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2answers
189 views

Symbolic matrix equation

I am looking to a system of equations of the form $\pi =\pi P$, the one encountered in Markov chain theory. My $P$ variable is: ...
3
votes
2answers
930 views

How to solve a “tensor equation”?

I am trying to solve equations which looks like this: $$ T_{ab} - T_{bc} = a_1 T_{ab} + a_2 T_{ac} + a_3 T_{bc}, $$ where $T_{xy}$ are tensors. I want to get the $a_i$'s (in this simple example ...
1
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1answer
128 views

How do I get Nsolve to work with hyperbolic functions?

This is a rather simple numerical solution, but it simply doesn't work. Does anybody have a solution? NSolve[x - Sinh[x] - 1 == 0, x] NSolve::nsmet: This ...
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3answers
3k views

How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
1
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1answer
399 views

General form of a linear transformation

Let $v_1 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}$ and $v_2=\begin{bmatrix} 1 \\ -1 \end{bmatrix}$ and let $A= \begin{bmatrix} 3 & 2 \\ -2 & 1 \end{bmatrix}$ be a matrix for $T\colon \Bbb ...
1
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1answer
675 views

Solving a nonlinear system of recurrence equations

I am having two problems regarding Mathematica, and both of them are happening because it does not accept such inputs: ...
1
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1answer
89 views

Find the point that holds a given property

I have a normal distribution with mean 106, and a standard deviation of 8. I'm being asked to find the point that has the property that 25% of these values have this value or lower. What I've ...
0
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1answer
270 views

Solve Probability of Distribution

Why does this work: Solve[Probability[x <= t, x \[Distributed] NormalDistribution[]] == 0.95 ,t] But this doesn't: ...
3
votes
1answer
619 views

FindRoot giving false roots with Bessel Functions

I have read in some places about the errors associated with FindRoot, but the closest thing I can find on this website seems to be due to the imaginary unit. I am dealing with what should be a ...
9
votes
3answers
490 views

Using NSolve in the complex plane

I am trying to find numerical values for $\Im\ e^{\frac{1}{2} +i\ y} = \Im\ \zeta(\frac{1}{2} +i\ y)$ for a given range. I have tried: ...
1
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0answers
409 views

Solving asymptotic equations

Let's say I have several equations that have solutions given as a negative series $$y(t,x)=\sum_{n=-1}^\infty a_n(t) x^{-n}=a_{-1}x+a_0+a_1x^{-1}+\mathcal{O}(x^{-2})$$ My equations look like ...
1
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0answers
84 views

Simple Solve example fails: why? [duplicate]

Solve is an amazing tool, but sometimes it doesn't work in the way I expect it to. The particular instance that is confusing me right now is this: ...