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

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1answer
60 views

System of polynomial equations with Solve does not converge

The Exp-method [1] is an analytical solution method for differential equations. Essentially, the method boils down to the solution of a system of nonlinear polynomial algebraic equations. In [1] (and ...
0
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0answers
34 views

Why differential equation reduces? [duplicate]

I am trying to ND-Solve the following equation: eqns = {x''[t] == -x[t], x'[0] == 0, x[0] == 4} The problem, is when I enter it, Mathematica reduces it to <...
1
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1answer
60 views

Precision in calculation [duplicate]

I am writing some code to demonstrate the effect of the number of significant figures a coefficient has on the solution of a nonlinear equation. I define the coefficient as follows: ...
0
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1answer
90 views

NDSolve for a system of nonlinear coupled pde

I try to solve a system($n$) of coupled nonlinear 1-d PDE's which is basically coupled sine-Gordon equations (through 2nd spatial derivative) in time and space. I am interested in the dynamics when I ...
0
votes
1answer
101 views

Find partial solution for underdetermined system of Boolean equations (Minesweeper)

In this article about creating a Minesweeper solver, the author talks about using matrices to solve given portions of a Minesweeper board. While reading that, I thought of a different way to limit the ...
5
votes
1answer
408 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 ...
2
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0answers
54 views

Estimating processing time for commands

I am trying to evaluate some equations by using Taylor series of expansion (Series[], ExpandAll[], and Normal[] command), and using n equation and n unknown (Solve). Following is not full command (if ...
0
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1answer
85 views

Solve non-linear system of 16 equations [closed]

I need a solution to a non-linear system of 16 equations, I am trying the following command and nothing is happening: ...
-1
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1answer
66 views

How can I solve a certain statics problem [closed]

Does someone have any idea how to solve it or from where to start?
0
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1answer
50 views

Symbolic Maximization: does not work with symbolic power?

Simple question from a beginner: I seem to be unable to do maximization if the variable has a power specified symbolically instead of numerically? ...
2
votes
1answer
103 views

How to approximate the solution of a system of quartic equations

In an attempt to evaluate the point at which the cycle 2 becomes unstable for the given map: \begin{equation} x_{n+1}=μ-x_n^4=f(x_n), \quad μ \in \mathbb{R} \end{equation} I have so far managed to ...
2
votes
1answer
48 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 ...
3
votes
3answers
189 views

Determine integer results using Solve

I'm trying to solve a Pythagorean pairs for m and n (for m and n < 100) which give integer p values in the following equation: Sqrt[m^2 + n^2] == p I may ...
5
votes
4answers
1k views

An easier way to find the properties of an ellipse from its equation?

In this Q&A about fitting an ellipse to a set of points, there are multiple answers that generated general equations of the ellipse, like this one by @ubpdqn: However, the steps to find out the ...
5
votes
1answer
106 views

SystemException[“MemoryAllocationFailure”] Uncaught SystemException returned to top level from NSolve

Bug introduced in 10.0.0 When trying to solve 8 equations in 8 unknowns, I get SystemException["MemoryAllocationFailure"]. I am not sure if I am doing something ...
5
votes
1answer
92 views

Passing starting values to FindRoot when called by the Shooting Method of NDSolve

According to the documentation of the NDSolve Method -> "Shooting" option, it is possible to pass to ...
1
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1answer
101 views
0
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0answers
36 views

Solving an inequality with Root objects

Given q1 = Root[(48 a^2 + 16 b) #^4 - (40 a^3 + 168 a b)#^3 + (-45 a^4 + 225 a^2 b + 72 b^2) #^2 + (27a^3 b - 162 a b^2) # + 27 b^3 &,1] Now, I know that the ...
1
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1answer
64 views

Is this expression solvable and if so is there a better way to do it?

I would like to solve this polynomial of third order for its roots: ...
1
vote
2answers
60 views

Solving simple transcendental equation [duplicate]

I would like to solve Tan[x] == 1/x Solve[] does not work, suggesting that there is no nice analytical solution for x. Surprisingly, NSolve[] does not work ...
6
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2answers
159 views

NDSolve and matrix formulation do not produce the same result. Why and which is more precise?

Let's assume a vector of variables $\vec a=(a_1(t),a_2(t),a_3(t))$ and let's assume a following DE$$C\ddot{\vec a}=B\dot{\vec a}+A\vec{a}+\vec F.$$ If $A$ and $C$ are both reversible, than the DE can ...
1
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2answers
66 views

Mathematica shows complex roots while asked for reals?

I ran the following code in Mathematica ToRadicals[Reduce[-14848 c^4 + 38016 c^3 x - 30888 c^2 x^2 + 6480 c x^3 + 1215 x^4 == 0 && c < 0,x,Reals]] ...
0
votes
0answers
32 views

Different root objects

Consider the quartic polynomial $$(48a^2+16b)x^4-(40a^3+168 ab)x^3+(-45 a^4+225a^2 b+ 72b^2)x^2+(27a^3 b - 162 ab^2)x+27b^3, \qquad (*)$$ where $a<0$. Consider ...
-1
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1answer
34 views

How can I get all the possible solutions using NSolve [closed]

How can I get all the possible solutions using NSolve. The following equation has eight analytic solutions. These analytic solutions are obtain using "Solve" as ...
1
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0answers
62 views

Obtaining values from interpolating functions

A similar question has been asked in the post HERE but the current question is more complicated: I have the following differential system ...
0
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1answer
86 views

problem in solving equation

this happened to me when I try to get (f) which should equal sqrt(3)/2 is there any problem in my formula or what? ...
1
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0answers
95 views
0
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0answers
40 views

NSolve with a term that is an interpolating function

I need to solve this system of equations Log[np[x]] + psi[x] + f[np[x], nm[x]] == 0 Log[nm[x]] - psi[x] + f[np[x], nm[x]] == 0 For ...
2
votes
0answers
52 views

Unusual error message from Solve when called by DSolve

Question 111150 presents an equation nonlinear in its leading derivative ...
1
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1answer
42 views

How to solve from a list

I have this equation: $y(t)=aE^{-bE^{-ct}}$ and I have this list: ...
1
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1answer
48 views

Maclaurin Series - Table

I'm starting to learn Mathematica. I have to solved this eq and draw the graph. It is developing a series of Taylor in about x0 == 0. This is my equation to solve ...
-1
votes
2answers
100 views

linear system equation ( trying to solve ) [closed]

I am trying to solve this system 3.7 x1+51.5 x10+71.3 x11-84. x2-16. x3-57.7 x4+89.7 x5-54.9 x6-85.8 x7+57.8 x8-51.3 x9==-36.8 -86.3 x1+5.7 x10-0.2 x11-39.9 x2+52.6 x3-45.6 x4+78. x5+90.7 x6-86.2 x7-...
0
votes
1answer
82 views

Maclaurin series [closed]

Can someone tells me, why is that not working? I'm starting to learn Mathematica. I have to solved this eq and draw the graph. It is developing a series of Taylor in about x0 = 0. ...
0
votes
1answer
54 views

Reduce in NDSolve [duplicate]

Second order ode; neither the trig RHS simplifies nor is the solution obtained readily: ...
1
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0answers
61 views

How to use interpolating functions in NSolve with a piecewise function?

I have a system of two non-linear differential equations that are piecewise, the solutions of which I would like to use to obtain the values of a third variable that is also piecewise. I have trouble ...
1
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0answers
89 views

Interpreting Root Objects [closed]

I have solved this system of equations in Mathematica for $x$ where the coefficients of the equations were functions of $a,b$ and $c$. Mathematica then displays real solutions $x$ with constraints on $...
5
votes
4answers
103 views

Using roots to get original equation

I have a list of four rules, that I would like to use to find the original polynomial that produced them. The rules are of the form ...
1
vote
1answer
36 views

One system consisting of multiple linear equations [closed]

Hello everyone i apologize if this has been answered before i honestly couldnt find it. The problem im having is that im trying to Define one system with multiple equations something like this: ...
3
votes
3answers
250 views

Why does FindInstance fail when Solve succeeds on these simple constraints?

Why does FindInstance[{a, b} > 0.27 && a == 10^8 && b == 2, {a, b}] fail even though ...
7
votes
4answers
480 views

How to find a tangent line with 2 points of tangency for a curve?

Say I have a function like this: f[x_] := 4 x^4 - 9 x^3 - x^2 + 10; Plot[f[x], {x, -1, 2}] It's obvious that there's a tangent line with 2 points of tangency ...
2
votes
2answers
93 views

How to find the integrand singularity points when having NIntegrate::slwcon:

In order to calculate the closed area of the curve below defined by parametric equation curve02, ...
30
votes
2answers
3k views

The Orbit and Perigee of the Flamsteed comet

Historical context This year we have the 330-th anniversary of the Battle of Vienna - one of the great formative events of European history, it took place on September 12, 1683. Kara Mustafa, Grand ...
0
votes
1answer
49 views

Extract solutions of linear system to variables

I need to output the answers from solve into the variables named just as they were named in the solve equations. I have checked out this thread Assign the results from a Solve to variable(s) but ...
1
vote
0answers
56 views

Artifacts in the solutions of NSolve [closed]

I have (what I think are) some problems with the precision of NSolve. I'm trying to solve this cubic equation: $a f^3(x)-b f^2(x)-c f(x)-z=0$ for the function $f(x)$ and then plot the following ...
0
votes
0answers
29 views

Finding parameters that give constrained eigenvalues of matrix

I want to obtain the eigenvalues $x_1,x_2,x_3$ of a hermitian, off-diagonal matrix, {{0, Conjugate[d], Conjugate[g]}, {d, 0, Conjugate[h]}, {g, h, 0}}, under the ...
2
votes
0answers
32 views

Solving for coefficients of a polynomial? [closed]

I'm sure I'm doing something wrong here, but I'm damned if I can figure out what. I'm trying to find a cubic function that passes through (0, 270), (1, 312), (2,230), (3,0), but the first way I tried ...
0
votes
1answer
86 views

How to solve a system of integral equations [closed]

I am trying to solve a system of equations as follows... f1[t]/3 == (1/3)[Integrate[f3[t], t]] f1[t]/(6/5) == Integrate[f2[t], t] f3[t] == Integrate[f1[t], t] I ...
0
votes
0answers
50 views

Output of NDSolve is useless when the system gets bigger

I have a bridge, which I want to discretize on $n$ stiff rods. To find a solution I wrote the following code in mathematica: ...
0
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0answers
37 views

Find Roots of expression with modified Bessel functions [duplicate]

I would like to solve an equation of this type $$A-B\,K_0(\kappa\,r)-C\,K_1(\kappa\,r)=0\ \ \quad \text{with}\ A,\,B,\,C,\,\kappa\in\mathbb{R},\ \text{known}$$ for $r$. I am not aware whether this ...