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

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4
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1answer
682 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
898 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
3answers
145 views

Regarding how to use Reduce

Say for example I am doing the following in Mathematica ...
4
votes
2answers
501 views

What is the efficient way to code Successive Over-relaxation (SOR) method in Mathematica?

I have written a SOR method (SOR is this method) code using C-style procedural loops. However, I think there might be (much) better ways to achieve the same end in Mma avoiding these loops. So my ...
4
votes
2answers
456 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
212 views

How to solve this trigonometric system of equations numerically?

How can the following trigonometric system of equations be solved numerically? ...
4
votes
2answers
178 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
3answers
205 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
1answer
3k views

Why can't Mathematica “Solve” my equation?

I am trying to get Mathematica to solve the following equality in terms of $w_i$ $\displaystyle \frac{\sum_{i = 1}^{n} x_i }{\sum_{i = 1}^{n} y_i} = \frac{\sum_{i = 1}^{n} ( (\frac{x_i}{y_i}) w_i ) ...
4
votes
1answer
174 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
4
votes
1answer
84 views

Solve or preferable Reduce equation

I am new to mathematica and trying to solve and reduce the following: Solve[1 - (1 - p^y)^(u (1 - p)) == a, y] or ...
4
votes
2answers
241 views

Why doesn't Roots work on a certain quartic polynomial equation?

In everything that follows I am using Roots to get the solutions to the equations. I start off with this equation: $$ \frac{A}{3}x^4 - x^2 + 2ax - b^2 = 0$$ Now ...
4
votes
2answers
149 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
1answer
189 views

Numerical errors/inaccuracies in ProductLog

Context In cosmology, a fairly accurate model to describe the gravitational potential, $\psi(r)$ of dark matter halos is given by $\psi( r)=\log(1+r)/r$. ...
4
votes
1answer
1k views

finding poles of a function

Is there a command to find the poles of a function $f=f(z)$? example: let $$f(z) = \frac{1}{z^2-1}$$ then we know that the poles are at $z=\pm 1$ but is there a special command in mathematica to do ...
4
votes
2answers
230 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
174 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
206 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
117 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
158 views

Check if an inequality holds among the solutions returned by Solve [duplicate]

Let's say I solve a system: Solve[{a == 3* c, b == 2 *a}, {a, b}] and then want to see if the values found for a and ...
4
votes
1answer
78 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
2answers
115 views

Specifying and solving a PDE on an L-shaped domain

I wish to solve Laplace's equation with Dirchlet boundary conditions on an L-shaped domain as described here http://www.inf.ethz.ch/personal/tulink/FEM14/Ch1_ElmanSyvesterWathen_Ox05.pdf I know how ...
4
votes
2answers
105 views

Can't solve equation having complex coefficients

Why can't Mathematica solve $\quad\quad\frac{1-i}{\sqrt{2}}=e^{i \alpha } \tan \left(\frac{\beta }{2}\right)$ with the restrictions $\alpha \in [0, 2 \, \pi)$ and $\beta \in [0,\pi]$: ...
4
votes
1answer
727 views

What do the hashtags represent in the result of Solve, and how should I use them? [duplicate]

There is a function that I'm trying to get the inverse of. My function is a simple polynomial: Tn[T_] := 4/9 T^3/Tc^2 + 5/9 T Now I tried to find ...
4
votes
1answer
518 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
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2answers
269 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
336 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
197 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
189 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
986 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
1answer
212 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
341 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
1k 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
2answers
326 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
213 views

What is the algorithm behind Mathematicas Reduce in this equation?

Mathematica can use Reduce to arrive at an answer in this equation ...
4
votes
0answers
215 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 ...
4
votes
0answers
148 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( ...
4
votes
0answers
114 views

Symbolic solution to ODE, pure InverseFunction not evaluated

I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
3
votes
2answers
273 views
3
votes
3answers
412 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 $$ ...
3
votes
3answers
140 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
460 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
691 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
3k 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
246 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 ...
3
votes
1answer
229 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 ...
3
votes
1answer
296 views

Simulating a quick return mechanism

Last time, I got a satisfying answer for simulating a toggle mechanism, just as expected. NDSolve is great. I tried playing with it (as a matter of fact, @MichaelE2 ...
3
votes
1answer
1k views

Finding intersection of two graphs

Here is a toy problem: I have a (directional) line that starts from {2,0} and goes through {1.8, 0.01}. Also I have a ...