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

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4
votes
2answers
843 views

How to find regions that satisfy this inequality?

I am new to Mathematica and would like to find the set $$\{ (x,y) \in \mathbb{R}^2: (3x+y\exp(xy))(x-a) + (6y + x \exp(xy))(y-b) < 0 \}$$ for some constants $a$ and $b$. How can I do ...
4
votes
2answers
145 views

Finding the parameter that makes real part of an eigenvalue of a matrix 0

I have the following 3x3 matrix: $\left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 \end{array} ...
4
votes
2answers
177 views

Find the value of parameter so that the equation has one solution

Let $(E_l) : x^4-4x^3+x^2(5-l^2)+4 x l^2-4l^2 = 0$ be an equation with $l$ as a parameter and $x$ as an unknown and $S_l$ the set containing all the real solutions of $(E_l)$. Then there is a unique ...
4
votes
3answers
260 views

How can I get the exact solution of this equation (inequality equation)?

I want to solve the equation and inequality equation $$\sqrt{8\cdot 16^x - \dfrac{1}{2}\cdot 9^x }= 3\cdot 4^x - 3^x$$ and $$\sqrt{8\cdot 16^x - \dfrac{1}{2}\cdot 9^x } \leqslant 3\cdot 4^x - 3^x.$$ ...
4
votes
1answer
364 views

How to solve this equation with integers as a solution?

I want to solve the equation $$x^y + y = y^x + x$$ with $x$, $y$ are integer numbers. I tried Solve[x^y + y == y^x + x, {x, y}, Integers] How to solve the ...
4
votes
2answers
407 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 ...
4
votes
2answers
736 views

Solving inequalities for positive Integers

Consider the following; ...
4
votes
4answers
679 views

recursively solve equation and saving the values

I am new to Mathematica. I am trying to recursively solve an equation and saving the values into a Table. Since I need the real solutions only I use ...
4
votes
2answers
404 views

Alternate parameterization of a line

There are several ways to specify a line. In Mathematica's graphics, it is done by specifying two points and then connecting the points with the Line command. But ...
4
votes
1answer
196 views

How to add equations' left and right sides together?

If we have two equations E1 and E2, and instead of using Solve to solve it, we simply need to manually add them up which would allow some simplification that could ...
4
votes
3answers
484 views

Inverting a Spline-Function (Bezier or BSpline)

I would like to use a Spline-Function to describe a transformation from one range of reals to another, that is I would like to have a function which maps a value $y$ on $x$ and for simplicity let us ...
4
votes
2answers
243 views

find where 3 inequalities are simultaneously greater than zero

I have 3 functions: f11[l], f12[l] and f13[l], and I would like to know for which values of ...
4
votes
2answers
334 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 ...
4
votes
1answer
593 views

Reduce an equation by putting a new variable

I have the following equation given: $$ (26-x)\cdot\sqrt{5x-1} -(13x+14)\cdot\sqrt{5-2x} + 12\sqrt{(5x-1)\cdot(5-2x) }= 18x+32. $$ In order to solve it, I want to substitute $t = \sqrt{5x - ...
4
votes
3answers
604 views

Replace function and its derivatives found with Solve

If I have an equation eq = f[x] + g[x] == 0 and I solve for f[x] sol = Solve[eq,f[x]] ...
4
votes
2answers
337 views

Why doesn't FindRoot work correctly?

I'm trying to find the roots of the following equation: I need to find λs for different values of ξ. I know that for all ...
4
votes
1answer
199 views

How to solve this trigonometric system of equations numerically?

How can the following trigonometric system of equations be solved numerically? ...
4
votes
1answer
256 views

Using external variable as a variable inside WhenEvent & NDSolve

I'm trying to use the new WhenEvent functionality of NDSolve in Mathematica 9, in order to perform an action when a variable in the system reaches a certain value. I would like this variable to come ...
4
votes
2answers
1k views

Select Solution with real (positive, etc) coefficients - ignoring variables

I often need to solve equations for numerical coefficients while preserving numerous variables (e.g. to preserve scaling relations). Thus I end up with a set of solutions like $$ ...
4
votes
2answers
160 views

Reduce with Integer domain, but receive a rational solution

I want to find the integer values $k$ so that D[f[x], x] has integer solutions. I tried ...
4
votes
2answers
168 views

Why the inequality does not take into account the domain?

I have this inequality: Reduce[(4000-1000k)/(k-4) < 0] and the answer is k ∈ Reals I would expect ...
4
votes
2answers
141 views

Is there a giant AND symbol/How to solve tons of equations simultaneously

$$\sum_{k=1}^na_k=a_1+...+a_n$$ $$\prod_{k=1}^na_k=a_1\cdot...\cdot a_n$$ $$\large{?}\small{_{k=1}^na_k=a_1~\&\&...\&\& ~a_n}$$ What in mathematica would allow me to index logical ...
4
votes
2answers
191 views

How can I eliminate equivalent equations from a list?

I want to find the numbers $a$, $b$, $c$, $d$ of the plane $ax + by +cz +d = 0$ which make the distance from the point $M(1,2,3)$ to the plane equal to 2. I tried ...
4
votes
1answer
115 views

Solving a nonlinear, second order d.e. in Mathematica

I am trying to solve the following differential equation $$ s''(x) = \frac{8}{9}s(x) -2s^2(x) + s^3(x), $$ with boundary conditions $s(-30) = 4/3 $ and $s(30)=0$, in Mathematica by using the following ...
4
votes
2answers
160 views

How to set up and minimize a large system of equations to resolve the individual components

I am trying to set up a system of 400*N equations to deconvolute spectral data for four different compounds. I monitored 400 different wavelengths in N solvents (3 solvents in this case). In order ...
4
votes
2answers
99 views

Non-convergance of the solution of the 1+1 partial differential equation

I am stacked with a partial differential equation as follows: This is the $\LaTeX$ expression for the equation $$ \frac{\partial y}{\partial t}=\frac{\partial^2 y(x,t)}{\partial x^2} ...
4
votes
1answer
73 views

Trouble using FindInstance with MatrixRank

I'm really confused about what's going wrong with my call to FindInstance: ...
4
votes
3answers
1k views

Backsubstituting solution into FindRoot

I am trying to solve a system of equations which is dependent to an parameter alpha. So I iterate over alpha via a ...
4
votes
1answer
419 views

How do I use RSolve to solve a system of recurrence relations?

I am trying to solve a system of recurrence relations as follows. ...
4
votes
2answers
226 views

Both Sin[x]==0 && Cos[x]==0 as a solution

If I do FullSimplify[Reduce[Sin[p1] == 0 && Cos[p1] == 0, Reals]] I get Cos[p1] == 0 && Sin[p1] == 0 ...
4
votes
1answer
300 views

pH calculations, speeding up code involving Solve

I'm trying to calculate pH values of solutions containing water and acetic acid. The relevant equations have been defined and I now want to find a solution using Mathematica. For a specific acid ...
4
votes
1answer
186 views

Asking Mathematica to produce a function of some variables

Given $$l_0=\sqrt{\frac{\lambda_1(\lambda_0+\mu_0)}{\lambda_0(\lambda_1+\mu_1-1)}}$$ and $$l_1=\sqrt{\frac{\lambda_0(\lambda_1+\mu_1)}{\lambda_1(\lambda_0+\mu_0-1)}}$$ ...
4
votes
1answer
156 views

How to demonstrate lack of stability with advection equation

I am trying to that using a coarse grid with an explicit method for, say, the advection equation leads to an unstable solution. The trouble is Mathematica avoids unstable solutions with good ...
4
votes
1answer
315 views

Use of $Assumptions [duplicate]

I don't really understand the behaviour and the usage of $Assumption. For instance, when I set $Assumptions = λ > 0, I expect ...
4
votes
2answers
346 views

Solution of equation with power series (perturbation)

So I need to use Mathematica to find the solution of $y=x- \epsilon \sin(2y)$ as a power series in terms of $\epsilon$. I'd assume I'd need to create an equation $f=x-y- \epsilon \sin(2y)$, then ...
4
votes
2answers
210 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 $a,b,\mu,\nu$ ...
4
votes
1answer
193 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 ...
4
votes
1answer
313 views

Eliminating functions from system of PDE in Mathematica

Mathematica users, Let's see an example of three PDEs: How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
4
votes
1answer
902 views

Efficient implementation of cubic equation of state

...In this case the Peng Robinson Equation of State. Equations of state are empirical equations with parameters derived from experimental data. They are used to predict pure component and mixture ...
4
votes
1answer
430 views

Solving recurrence relation using Mathematica defined in a piecewise way

I have a recurrence relation defined as following: RSolve[ { p[0] == p0, p[1] == λ p[0]/μ, p[i + 1] == λ p[i]/(2 μ) }, p[i], i ] Note that the relation ...
4
votes
2answers
213 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 ...
4
votes
0answers
653 views

Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
4
votes
0answers
120 views

Solving a nasty equation

Here's an equation that I need to solve for $t_k$ $$ \theta_0 = \tan^{-1}\left(\frac{2(w_x - m)}{p - g {t_k}^2 - 2 t_k w_y}\right) - {\frac{1} {r}} \left( \left(\frac{m}{t_k}\right)^2 + \left( ...
3
votes
2answers
269 views
3
votes
3answers
134 views

Find $Y \in (0, 5)$ such that the roots of $4x^2 + 4xY + Y + 2 = 0$ are real?

The problem is to find all $Y \in (0, 5)$ such that the roots of $4x^2 + 4xY + Y + 2 = 0$ are real. I took a straightforward approach with Mathematica with the intent of listing the only solutions ...
3
votes
1answer
396 views

How do I solve $1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x))= 0$?

Consider the equation $$ 1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x)) = 0 $$ where $A,B \in \mathbb{R}$ are constants. What is the analytic solution?
3
votes
3answers
530 views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
3
votes
2answers
2k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
3
votes
2answers
236 views

Mathematica does not understand (R^3)^(1/3) is the same as R [closed]

In the output from a calculation in mathematica stands a/((R^3*c)^(1/3)), with c and a ...