# Tagged Questions

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

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### 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 ...
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 <...
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### 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: ...
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### 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 ...
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 ...
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 ...
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### 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 ...
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: ...
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?
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### 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? ...
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: $$x_{n+1}=μ-x_n^4=f(x_n), \quad μ \in \mathbb{R}$$ I have so far managed to ...
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### 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 ...
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 ...
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 ...
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### 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 ...
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### 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 ...
101 views

### Different interpretation of system of equations

Given the variables ...
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 ...
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: ...
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 ...
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 ...
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### 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]] ...
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### 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 ...
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 ...
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 ...
17 views

### Step by step solution for x 2a^2-5ab-ax+2b^2-bx-x^2 = 0 [duplicate]

I need the step by step solution please.
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? ...
95 views

### Need help solving a polynomial system [closed]

I need help solving the following system of equations: ...
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### 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 ...
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### Unusual error message from Solve when called by DSolve

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

### How to solve from a list

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

### Reduce in NDSolve [duplicate]

Second order ode; neither the trig RHS simplifies nor is the solution obtained readily: ...