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

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5
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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 ...
4
votes
1answer
71 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
81 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
vote
1answer
92 views
0
votes
0answers
33 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
vote
1answer
63 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
52 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
votes
2answers
152 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
vote
2answers
63 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
votes
1answer
32 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
vote
0answers
56 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 ...
1
vote
0answers
42 views

List within a Do loop , i cant get any values [duplicate]

I am having the following problem. I am trying to get some values from solving an equation and apply them into a list but in the output I get nothing but the symbol of the variable... The code is as ...
0
votes
1answer
84 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
vote
0answers
94 views
0
votes
0answers
53 views

Why can't Mathematica solve something like this?

I'm trying a simple command like this: Solve[a[1] v[1] + a[2] v[2] == v[1] + v[2], {a[1], a[2]}, Integers] and getting an error message: ...
0
votes
0answers
36 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
47 views

Unusual error message from Solve when called by DSolve

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

How to solve from a list

I have this equation: $y(t)=aE^{-bE^{-ct}}$ and I have this list: ...
1
vote
1answer
47 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
91 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 ...
0
votes
1answer
80 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
52 views

Reduce in NDSolve [duplicate]

Second order ode; neither the trig RHS simplifies nor is the solution obtained readily: ...
1
vote
0answers
49 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
vote
0answers
82 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
101 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
33 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
247 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
470 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
90 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
2k 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
47 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
55 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
28 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
29 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
70 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
46 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
votes
0answers
36 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 ...
0
votes
1answer
52 views

Solving a System of Equations syntax confusion

I have a system of two equations which I would like to solve in terms of a third unknown variable $s$. ...
1
vote
0answers
33 views

Rearrange generic expression into a quartic polynomial

I'm rather new to mathematica. I'm attempting to express: $$\sqrt{x} = \frac{\gamma \sqrt{y}}{-i(\Delta - g \sqrt{1 - (\frac{\tau}{4lhx})^2})+\frac{\gamma}{2}}$$ as $$0 = Ax^4 + Bx^3 + Cx^2 + Dx + ...
0
votes
0answers
65 views

How to systematically approach when solving a large system of differential equations?

I defined several functions in order to get to the final system of a partial differential equations I have to solve. Here is how I did those definitions: ...
0
votes
1answer
34 views

“Solve” with problem “Solve::ivar: ”-1+t is not a valid variable.“”

Solve[{Ee1*ek1 + g*h*(1 + r) + j1*h*ek2 == ek1, Ee2*ek2 + j1*h*ek1 + j2*h*ek3 == ek2, Ee3*ek3 + j2*h*ek2 == ek3}, {r}] want to get ...
1
vote
0answers
48 views

Solving a system of equations and inequalities over the reals

I have to solve the following system: $$\begin{cases} 16x^4-40ax^3+(15a^2+24b)x^2- 18abx+3b^2 = 0 \\ 5ax-4x^2-b>0 \\ 15ax-20x^2-3b<0 \\ 4x^3-8 c x^2+5acx-cb <0\end{cases},$$ where $c<0$, ...
4
votes
2answers
203 views

General solution for a linear ODE set with complicated coefficient

This is the original problem that motivated me to ask this question. I encountered it when trying to reproduce the deduction in this paper. (I'll paste the relevant part below to make this question ...
1
vote
1answer
107 views

Is the output to Solve ordered or are the solutions randomly placed?

I am trying to find the roots of a polynomial of eight degree $$\sin^8\varphi-2\lambda_i^2\sin^6\varphi+(6\lambda_i^2+\lambda_i^4)\sin^4\varphi-(4\lambda_i^2+2\lambda_i^4)\sin^2\varphi+\lambda_i^4=0$$ ...
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
0answers
65 views

How do I invert a function with two arguments? [closed]

I begin with a function defined by c[u_, mH_] I won't go into details because it comes from countless lines of partial differential equations, boundary ...
4
votes
3answers
314 views

FindRoot constrained to maximum

I am using FindRoot to find the local maximum op some function, by examining where its derivative is zero. However, keeping the starting value the same, sometimes ...