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

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2
votes
1answer
130 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
1answer
97 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
460 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
87 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
544 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
126 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
149 views

Quadratic Equations mod p^k

As part of a larger program, I need to solve $A x^2+B x+C \equiv 0 \mod p^k$ for prime $p$. Right now I'm doing this by calling ...
2
votes
2answers
192 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
256 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
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 ...
2
votes
1answer
146 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
340 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
544 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
286 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
94 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
144 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
75 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
81 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
88 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 ...
2
votes
1answer
88 views

Fixed Points Problem with 2D Mapping

I have been playing with the mapping given by ...
2
votes
1answer
194 views

Problems with NDSolve and partial differential equations of several variables

Suppose we have the following partial differential equation: $$ 0 = \frac{ \partial w }{ \partial \tau } + \left( w + \sqrt{ h + \beta } \right) \frac{ \partial h }{ \partial \chi } $$ where $w$ = ...
2
votes
1answer
157 views

How to figure out whether a nonlinear inequality holds or not

I have an inequality consisted only of seven parameters as follows: $(1 + g)^{-(m+w)}\big[\big\{a+(1-a)(1 + g)^m\big\}(1 + p q)Q - (1 + g)^w \big\{(1 + g)^m (1 + q)-(1-p)q\big\} Q\big] < 0$ ...
2
votes
1answer
182 views

How to solve three equations with four unknowns iteratively?

I have three equations of the form $\quad \eta = f(N1L, N2L)$ $\quad N1L = g(\eta, R)$ $\quad N2L = h(\eta, R)$ I want to eliminate $\eta$, so that I can get $N1L$ and $N2L$ for a range of $R$. I ...
2
votes
1answer
128 views

NSolve for system of polynomial equations

I would like to find all the solutions to the following system of 8 polynomial equations for the variables w1, w2, w3, w4, w5, w6, w7, w8 ...
2
votes
1answer
60 views

Solve[ ] for 2 variables not returning list of two variables

I type into mathematica: Solve[2 Sin[(Sqrt[3] x - 3 y)/2] == 2 Sin[(Sqrt[3] x + 3 y)/2], {x, y}] expecting it to return a list of pairs of solutions of the form ...
2
votes
1answer
121 views

Equation involving hypergeometric functions

I want to solve this equation but nor NSolve nor Solve are able to do this. ...
2
votes
2answers
573 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
145 views

Deriving least-squares equations in Mathematica

I define $Y = a + b*x + e$, and I want to find values for $a,b,$ by least squares, so I minimize $RSS = sum((Y_i - a - b*x_i)^2)$ I then take derivatives, ${d RSS \over da} = 0$ and ${d RSS \over db} ...
2
votes
1answer
111 views

FindRoot: Minimum Execution Time

Is there a minimum execution time for the command FindRoot? If so, can I get rid of it? For example, if I compute the time to solve the fundtion x=0, it takes around 0.27ms per evaluation: ...
2
votes
1answer
166 views

Simplify equation using conditions/inequalities

If I have an equation like f[x](1 + a)==0 I'd like to be able to tell Mathematica that 1+a doesn't vanish in general, and get back ...
2
votes
1answer
127 views

Declaration of variables in large Linear Programming model with NMaximize

I want to solve a large LP problem using NMaximize. This is a small instance of my bigger problem: $$max \sum^{4}_{t=1}(\sum^{4}_{c=1} V_{c}*f_{c,t})\\ s.t\quad ...
2
votes
1answer
116 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 ...
2
votes
1answer
140 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 ...
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
votes
2answers
1k 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
1answer
507 views

How can I solve an exponential inequality in Mathematica?

I would like to solve the equation: A Exp[m t + s Sqrt[t] x - 1/2 s^2 t] >= K with respect to x (which is in the exponent) ...
2
votes
1answer
481 views

Reduce/Solve an equation with symbols in powers

I am trying to solve the following equation with respect to x. eqn = x^z + y == a; But when I do ...
2
votes
0answers
45 views

Is FindRoot wrong about its WorkingPrecision?

I noticed an odd mismatch between the behaviors of NDSolve and FindRoot. If you give NDSolve an equation of a certain precision, say 20, and tell it to use a higher WorkingPrecision, say 30, it will ...
2
votes
0answers
49 views

Problem with plotting a function that calls FindRoot

I am having difficulties in plotting the solution of FindRoot to solve 4 variables. I defined a function and then tried tp plot it, but got an error message ...
2
votes
1answer
56 views

Plot directional field with a initial vlue

I do not have enough reputation to comment on other questions, hence I have to ask my own one I want to solve the following nonlinear first order ODE, $$(1 + x) (0.5 y[x]^{-0.5} (x - y[x])^{0.5} - ...
2
votes
0answers
62 views

How to handle solution returned by ParametricNDSolveValue in FindRoot

i was trying to solve a problem relative to root finding in a system of differential equations; here's a simpler case. With two distinct set of parametric differential equations, i'm able to find the ...
2
votes
0answers
71 views

Simplify large fractions

Hi i'm quite new with Mathematica and i'm experiencing some problems with Simplify and FullSimplify. I'm dealing with a sistem ...
2
votes
0answers
97 views

NDSolve is running an extremely long time: how can I save the existing data?

I am trying to solve a PDE by the following code. It takes 1 hour or so to reach t=25.72 but about 20 hours to reach t=25.72404031638060174049337306126853310997. Actually, the time step is extremely ...
2
votes
0answers
125 views

Proving large inequality in 6 variables

I have arrived at a very large inequality in 6 variables that I would like to prove is true. The command I have tried is the following: ...
2
votes
0answers
142 views

Apart for complex roots?

Let p[x] be a polynomial in x and consider the partial fraction decomposition of 1/p[x]. ...
2
votes
0answers
141 views

What are the steps using boolean algebra for transforming one equation into another?

I have a special case where I have two equations, which I have solved in a better and quicker way, but I need to solve with Boolean algebra. Using the laws of Boolean algebra, I have to prove that ...
2
votes
0answers
184 views

Fitting an implicit function to data with error bars [closed]

I am trying to fit a Brillouin function to the peak intensity of neutron scattering data, for which I have an error bar for each data point. For this the program has to fit a function, for which the ...
2
votes
0answers
89 views

How does Mathematica resolve symbolic systems of inequalities?

Before getting into my (probably annoying) question, let me provide some context: I recently started using Mathematica to automatically perform stability analyses that I previously did by hand. A ...
2
votes
1answer
65 views

Plotting Multiple Solve Functions

My goal is to plot the functions returned from Solve but assigning each solution to a different function. Here is an example where I do it by hand ...
2
votes
0answers
263 views

Solving a system of two nonlinear equations with many symbolic parameters

I have two nonlinear equations with two unknowns, $x$ and $y$, and many symbolic parameters, $a, b, c, d$. They look someting like: $\frac{1}{x}(1+x)^a (1-b)(cx+dy)=0$ ...