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

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2answers
793 views

How to make a Dynamic Calculator to solve a quadratic equation?

Taking my first steps in the world of Mathematica Programming. The aim of my program was to modify Wolfram's dynamic calculator (which performs an addition subtraction and a product - in response ...
2
votes
1answer
462 views

DSolve expression doesn't evaluate

Can Mathematica solve $\; d^2/dx^2{}+ (1/x) d/dx\;$ form of equations? For example, I am trying to solve the system of equations given below: ...
2
votes
2answers
2k views

How could I define a function as the solution of equations in Mathematica?

I have posed a specific question yesterday but it may be too trivial to answer. I think the question could be asked in a more general way so it is easier to answer. Then I could solve the original ...
2
votes
1answer
236 views

Finding the root of a nested function with small values

I have reduced an error in my program to this line of code: FindRoot[Nest[# (1 - #) k &, 1/2, 2^4] - 1/2, {k, 3.5}] It works for $2^1, 2^2, 2^3, 2^4,$ but ...
2
votes
2answers
2k 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 ...
2
votes
2answers
557 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
144 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 ...
2
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2answers
595 views
2
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1answer
2k views

'not a valid variable' error when trying to solve 13 equations with 13 variables

I want to solve 13 variables by 13 equations. And here is my program: ...
2
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1answer
48 views

Finding an Integer, Unimodular Matrix that connects two given matrices

I have two symmetric, integer matrices, $K$ and $K_2$ which have the same determinant and the same signature (number of positive - number of negative eigenvalues). I want to find an integer valued ...
2
votes
1answer
119 views

Differential Equation with Numerically Integrated Boundary Conditions

I have a second order differential equation that I'd like to solve numerically, and then integrate its solution twice to get the parametric equations of a curve. The ODE is: $2 ...
2
votes
1answer
47 views

Passing a list to a nested vector function

In order to apply a newton-rhapson algorithm to solve a set of nonlinear vector equations such as these, f[x_, y_] = {x^2 - 3*y + 6, (y + 1)^2 - x - 33} I need ...
2
votes
1answer
84 views

System of differential algebraic equations with one of the variables as an argument of the other varaibles

This is my first question here and I don't even know what to search for to find a solution. So I'd appreciate it even if someone can point me in the right direction. EDIT: My post had many problems, ...
2
votes
1answer
66 views
2
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1answer
76 views

Can not Solve FinancialDerivative for volatility

Although Solve can solve FinancialBond for an input parameter (e.g. par) given the price of a bond: ...
2
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1answer
129 views

How to handle a special Neumann-like boundary condition in NDSolve?

How to solve the following nonlinear ODE with two algebraic equations and one boundary condition? ...
2
votes
1answer
77 views

Can't obtain Real results using NSolve

I am trying to find the critical properties of the Carnahan-Starling equation of state, $$p=\rho R T\frac{1+b\rho /4+(b\rho/4)^2-(b\rho/4)^3}{(1-b\rho /4)^3}-a\rho^2$$ using this system of equations, ...
2
votes
1answer
98 views

Reduce not solving linear equation

I have a long equation in 7 variables but the equation is linear (affine) in x. But when I try to solve with Reduce, it keeps running forever. With Solve, I am able to get an answer. Usually I have ...
2
votes
1answer
110 views

How to plot a figure according to two equations?

There are two equations like this: $a=f(x,y)$ and $z=g(x,y)$, where $a$ is a constant. In principle, one can solve $a=f(x,y)$ for $y$ as $y=k(x)$ and substitute it into the second equation to obtain ...
2
votes
2answers
73 views

How to use the variables from Table in calculation

New to the site and Mathematica. I'm trying to use the finite element method to get a temperature profile. So if $q_0=f(T_0,T_1)$, $q_n=f(T_{n-1},T_n)$ and we also know that ...
2
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1answer
184 views

How to properly interpret a seemingly contradictory result in Mathematica?

I have a problem with interpreting the results of my notebook outputs. It is important that I do not err with the interpretation. Here is the full input: ...
2
votes
1answer
199 views

NDSolve doesn't work for this simple differential equations

I try to use NDSolve to do this partial differential equations, but the result is wrong... The source term is a Gaussian pulse as time and an exponential decay with the depth z. The result should be ...
2
votes
1answer
255 views

Stability Boundaries via Routh-Hurwitz Criterion

I'm attempting to determine the stability boundaries of a 2nd order system via Routh-Hurwitz stability criterion. That is to say, I need to compute when a polynomial, which is in terms of variables ...
2
votes
1answer
108 views

Find tangency of InterpolatingFunction and circle

I am trying to use a system of equations to solve for the common tangent of a (polar) InterpolatingFunction and a circle. Unfortunately, both NSolve and FindRoot don't yield results, even when I ...
2
votes
2answers
195 views

How do I get all the roots within a certain range for an equation? [duplicate]

I wish to find ALL the roots of the following equation $ x \tan(ax) - c = 0$ within a range, where a and c are constants I control. I've been using ...
2
votes
1answer
157 views

Symbolic quadratic constrained maximization with non-negativity constraints?

Dear Mathematica users, I attempted to maximize the below quadratic function K, subject to x1+x2<=A, and a series of ...
2
votes
2answers
309 views

How to find roots of a system of equation when number of equations and variables don't match?

I'm trying to check if a system of equations has a solution around a given point, the problem is that I'm using FindRoots and doesn't work when there are a different number of equations and variables, ...
2
votes
1answer
147 views

FindRoot over a domain, but give domain boundary if no root exists

I call r = x /. FindRoot[f[x] == 0, {x, 0, -5, 5}] f[x] is always monotonic, but sometimes it doesn't have a root in the ...
2
votes
3answers
757 views

Backsubstituting solution into FindRoot and Plot

I want to find roots from a transcendental equation using FindRoot as a function of a real parameter and then plot the solutions vs. the parameter. The following commands work perfectly: ...
2
votes
1answer
96 views

Strange behavior using variable in Exists

I came across a behavior that doesn't make sense to me when I tried to use Exists in Reduce. If I run commands: ...
2
votes
1answer
523 views

Why does Mathematice dislike my boundary condition in NDSolve?

im trying to solve a PDE-System, with the "periodic boundary condition" c[t,0]==4*c[t,2pi] But mathenmatica says: NDSolve::bcedge: "Boundary condition ...
2
votes
2answers
893 views

Solving simultaneous exponential equations

In[1]: Solve[{(1 + k)^n == 0.6, (1 + k)^(n + 1) == 0.3}, {n, k}] Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; ...
2
votes
1answer
728 views

2d heat conduction equation: Boundary and initial conditions are inconsistent

I have the following code for a 2d heat c equation: ...
2
votes
1answer
130 views

Visualizing how the zeros for this function change as its input parameter changes?

I'm trying to explore how the zeros of a certain parameterized function change as its parameter changes. ...
2
votes
2answers
211 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
1answer
433 views

Solving this system of equations produces an error message about badly conditioned matrix

I want to determine a balance distribution. Ü = {{0.4, 0.2, 0.3}, {0.3, 0.5, 0.2}, {0.3, 0.3, 0.5}}; and ...
2
votes
1answer
2k 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 ...
2
votes
1answer
152 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: - $$k^2-2 k x+x^2$$ ...
2
votes
2answers
409 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
1answer
680 views

Defining regions for `Exclusions`

I have the following function I want to plot in 3D (For simplicities sake we can say $a=5,b=-1,c=3$.) ...
2
votes
1answer
330 views

How to solve a symbolic equation with symbols in powers

I am trying to solve $\dfrac{\rho\ ((1-b)\ \lambda _f\ \lambda _s\ P _A)^{\rho }}{b-1}+\dfrac{\rho \left(\dfrac{b\ \text{ps}\ x}{1-\text{ps}}\right)^{\rho }}{b}=0$ in terms of $b$, I ...
2
votes
1answer
90 views

Putting as many expressions as possible equal to zero

Say I have a list of expressions involving many different variables. I would like to see how many of the expressions I can set equal to zero thereby solving for some of the variables in terms of the ...
2
votes
1answer
218 views

Constant Heat Flux Boundary Condition for the Differential Heat Equation

I am attempting to solve the transient heat equation for a very simple geometry and I am getting a junk solution. I have identified two distinct regions (wall and super-heated fluid layer) with their ...
2
votes
1answer
102 views

Solving a consistent overdetermined linear system

Not a duplicate question. I already tried all the Answers offered for this Question and they failed, so I believe this is a different problem with Solve[]. I have ...
2
votes
1answer
196 views

Solving SDE: $\frac{dy(t)}{dt}=(c+\sigma_wW(t))y(t)+\epsilon(t) $ in Mathematica

I want to solve this differential equation $\frac{dy(t)}{dt}=(c+\sigma_w W(t))y(t)+\epsilon(t) $. For details see ...
2
votes
1answer
122 views

Solve an inequality involving a sum with a parameter

Good day. I am new to Mathematica and I am looking for advice. Is it possible to solve $$\sum_{k=0}^{n} \frac{p^k}{k!}>0$$ for $n$ where $p$ is a parameter? When I do ...
2
votes
2answers
158 views

Solving a system of weird equations

I'm trying to have Mathematica solve a system of equations for a friend's work in Computer Vision. I'm essentially going in blind to this and am not very familiar with Mathematica syntax, so would ...
2
votes
1answer
98 views

Reduce / Solve cannot solve simple equation

Why does Reduce[{a^b*c^b == c, 0 < b < 1, a > 0, c > 0}, c, Reals] give ...
2
votes
1answer
102 views

Can't NSolve system of exponential and linear equations in several variables

At the moment I am stuck with the following code, when specified to use root , quadratic or log utility functions all it fine, only exponentials like: $\small \left\{-e^{-c_{0,1}}-0.25 ...
2
votes
1answer
98 views

How to solve for the closed form of this recurrence?

For integers $L,k \geq 0$: $$T(L,k) = \begin{cases} 0 & \text{if }k \geq d, \text{ever}\\ -a_{k} & \text{if }L=0 \text{ and } k<d\\ a_dT(L-1,k+1) - a_{k}T(L-1,0)& \text{if } L>0 ...