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

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100 views

Why does Mathematica not evaluate the difference recurrence using `RSolve` or `RecurrenceTable`?

Mathematica does not evaluate the following recurrence of two variables using RSolve and only echoes the input: ...
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1answer
76 views

using FindRoot with a Module that takes a parameter

Observed an error when calling a Module from FindRoot. I created a module which first solves a differential equation and then returns the value of that differential equation when the independent ...
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2answers
59 views

RegionPlot after Reduce

I have a problem in this form To solve this I have tried this f1[y_] := 2 - (y - 1)^2; f2[x_, y_] := x + 1 - (y - 2)^2; f[x_, y_] := Max[f1[y], f2[x, y]]; The ...
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1answer
283 views

How to plot the graph of the equation F[x,y]=0 if y is real number, x is complex? [closed]

I have an equation F(x,y;a,b,c,...)=0, where x and y are variables, a,b,c,... - parameters. y is a real number, x - complex. For every given y I need to solve this equation, i.e. to find Im(x) and ...
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1answer
90 views

Plot roots of polynomial system of equations in 3 variables

I have the two equations $x^2 + 2y^2 + z^2 = 1$ and $xz -y^2 = 0$ I want to plot the roots in 3D. i.e the coordinates $x,y$ znd $z$
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1answer
298 views

4th-order Runge-Kutta method to solve a system of coupled ODEs [duplicate]

I am a beginner at Mathematica programming and with the Runge-Kutta method as well. I'm trying to solve a system of coupled ODEs using a 4th-order Runge-Kutta method for my project work. I have ...
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2answers
368 views

Defining the domain of positive real numbers

I am trying to solve an equation by assuming that all the variables are real and strictly positive. I can use the keyword Reals for the argument ...
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2answers
112 views

Solving matrix equation

How can I solve the forward equation S[t]=C+A*S[t+1]*(Inverse((I-B*S(t+1)))*A for t=1 to t=10 and ...
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2answers
71 views

Finding roots of a function with a varying parameter

So I'm brand new to Mathematica, and basically what I want to do is find the roots of a function at varying time intervals. The function I'm using is: ...
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3answers
112 views

NSolve & PrecisionGoal

I am using NSolve to find numerical solutions of a particular equation. I do not need the solutions to as high of a precision as the other numbers in my notebook. To improve run time (I am iterating ...
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2answers
494 views

How to obtain all solutions for Cos[x] Cosh[x] == 1?

Both analytical solutions or all numerical solutions are good enough. FindRoot may be a possible solution, any better solution? ...
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1answer
126 views

strictly positive solution to $Ax=b$

How to find in mathematica one real strictly positive solution, if any, of $Ax=b$. A is rectangular matrix. Thanks
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1answer
130 views

Why is ((v k)^-n (k v^n - v k^n))/(n - 1) == b so hard for Mathematica to solve (for v)?

I've tried using both Solve and Reduce. For something that takes maybe 3 minutes to solve with paper and pencil, I'm very ...
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3answers
87 views

`Solve` with variables as single vector

Say I have a set of equations where the unknown variables are the elements of a vector $c=(c_1,c_2,\ldots)$ and want to solve it for $c$. Is there a way to do this with ...
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1answer
62 views

Export data from NDSolve when they meet a certain condition

I need to export to a txt file the data from the following system of equations: ...
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1answer
77 views

Getting unwanted solution from Solve

I am solving the simultaneously equations $\quad \quad x_7=0$ and $\quad \quad 6x_4x_5+6x_3x_5x_6+zx_4x_7^2+zx_5x_7^2=0$ with Solve. Here, $z$ is an unknown ...
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1answer
106 views

Applying N to the roots found by Solve gives complex numbers when the roots are real [closed]

I have a function which is f(x) = x^3 - 5 x^2 - x + 1. When I solve for x to find the zeros ...
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1answer
148 views

Eliminate z from two equations in x, y, z and plot y as a function of x [closed]

I have this equation to begin with: $$1 - 3 x y = 5 z - 2 x $$ I want to solve this equation for $z(x,y)$, then plug $z(x,y)$ I plug $z$ inside a second equation: $$ y = 7 x z - \frac{z}{x} $$ ...
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1answer
162 views

Solving equations with QuantityVariable

I'm trying to understand how to easily solve equations that use QuantityVariable. Why does this fail? ...
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1answer
63 views

Some question on “Reduce”

Is this my mistake? I am trying to solve ...
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1answer
57 views

Can someone please help me to state assumption?

I am currently trying to solve under what condition does the following term will be zero? ...
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1answer
288 views

How to solve a complicated equation system

I am trying to solve the equation system eq1==eq2 for $\sigma1$ and $\sigma2$ where eq1 and ...
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1answer
248 views

How can I find a root of my transcendental equation near a certain point?

What function could I use to solve this equation for x: E^(-x^2) = 1 - Cos[x] I tried Solve, ...
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1answer
219 views

Solution of an ODE in implicit form

For some non-linear ODEs there is only implicit form of solution using DSolve. For example DSolve[(y[x] + x - 1)*y'[x] - y[x] + 2 x + 3 == 0, y[x], x] gives ...
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2answers
243 views

Symbolic solution of irrational equation

Is there any a nice looking solution to the following equation? eq[x_] := 2 x q1 - 2 q2/x^3 - (4 x^3 q3 - 4 q5/x^5)/(4 Sqrt[x^4 q3 + q4 + q5/x^4]) Better than ...
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1answer
76 views

Invariant error plot for an arbitray system of ODE

i try to use InvariantErrorPlot command for a generic system of ODE but i find only example with pre-building equations from Mathematica Packages. This is one of ...
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1answer
271 views

How to do Inverse formulas/Rearrange formulas in Mathematica? [duplicate]

Hi am a student in chemical engineering and I have the necessity to rearrange formulas algebraically, for example ...
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1answer
87 views

Asymptotics of sum of binomials

I would like to find the asymptotics of Sum[Binomial[n,i]*1/i^((n+1)/2),{i,1,n}] I saw Find asymptotics of Sum[2^i*Binomial[n-i-1,2*n/3-1],{i,0,n/3}] but I ...
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1answer
152 views

Solve returns a wrong answer

I'm afraid the following is rather localized questions, but I don't know how to simplify and generalize it. I have the following two points (in the real plane): ...
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1answer
103 views

Solve failing and not clear why

I define the function: w[q_, n_, a_] := q/(4 Pi n r^2) (1 - Exp[-2 r/a] (2 (r/a)^2 + 2 (r/a) + 1)) I then want to solve: ...
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1answer
229 views

FindRoot equation-variable mismatch

I cannot figure out why FindRoot doesn't work and returns this error: The number of equations does not match the number of variables in ... My problem: drawing ...
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1answer
241 views

Equating and solving equations that have been generated using table[]

I am in the process of trying to use Mathematica to find the coefficients of transmission and reflection for the wavefunction of a beam of particles tunnelling across any number of identical potential ...
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1answer
541 views

How to guess initial complex value for FindRoot

I have to solve a transcendental equation for a parameter, say $\beta$. Now, the $\beta$ has a range from $ik$ to $k$ where $i$ is the usual imaginary root $\sqrt{-1}$ and $k$ is a real number. ...
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2answers
616 views

Rearranging an equation with the sine function in it [closed]

When I evaluate Solve[a==Sin[b*c], b] to rearrange the following for $ b $: $$ a = \sin(bc) $$ I get the following result from Mathematica: $$\begin{align*} ...
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1answer
2k views

How to solve a simple inequality

I am having trouble getting Mathematica to solve really simple inequalities. I started with Solve[{y^x >= 2*y - 1}, x] but Mathematica can't solve it. So I ...
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1answer
464 views

Solve equation with inequalities for parameters

I want to solve following equation: ...
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3answers
383 views

equation solving problems

I have some equation: $$ veq=-2-lr-l^2r+2(r+ir^3\omega) v' + (-2+r)r^2v'^2 + (-2+r) r^2 v''==0 $$ or in Mathematica form: ...
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2answers
62 views

Condition on Inside of Region

How do I handle boundary conditions present in the region. Mathematica complains about the condition v [1 , t ] == u [1,t]. The condition should be given to this ...
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1answer
61 views
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1answer
100 views

How to solve a certain coupled first order PDE system

I would like to find the solution $(U,V)\equiv (U(x,t),V(x,t))$ of the following system. \begin{equation} \displaystyle\left\{\begin{array}{l} \frac{\partial U}{\partial t}+(a+b x)\frac{\partial ...
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3answers
120 views

NSolve returning an empty set

Dear Mathematica experts. I am a chemist looking to use Mathematica to solve a system of equilibrium equations. I have a system of 8 polynomial (I think) equations with 8 unknowns, yet when I use ...
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1answer
69 views

Trying to find solution for system of ordinary differential Equations [closed]

I've got 2 functions: A'[t] = (0.5/(1 + (B/k1)^n)) - 0.2*A B'[t] = (1/(1 + (A/k2)^n)) - 2*B with conditions of ...
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1answer
125 views

Approaches to solving non-linear systems of equation with assumptions

The specific type of system looks as follows: \begin{align} (r-r')x+4d_1 x^3+4d_{12}xy^2 &= 0 \\ (r+r')y+4d_2 y^3+4d_{12}yx^2 &= 0 \\ \end{align} Where $r,r',d_1, d_2, d_{12}$ are all real ...
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1answer
99 views

Solving equations bounded by a region

Straight to the point I have a function ...
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1answer
85 views

Complicated equation solving

I want to find the maximum point or optimal value $y$ of Rx1[y_, a_, b_]. ...
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1answer
86 views

Optimizing matrix inequalities over trace

I need to solve the following problem. Given $n \times n$ Hermitian matrices $A\geq 0$ and $B_1, ~ B_2$ (need not be positive semidefinite), with $Tr(AB_1)<0~,Tr(AB_2)<0$ construct a ...
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1answer
204 views

Why won't mathematica solve my two simultaneous equations? [closed]

I'm trying to solve for two unknowns with two equations as follows; ...
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1answer
81 views

Elimination returning true instead of correct answer

I define the following functions: ...
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1answer
80 views

How to solve these equations by Mathematica?

l tried it with Solve,DSolve and NDSolve functions,but all failed.Should l simplify the equations in the papers or use other mathematica functions.Thanks~
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2answers
147 views

Intersection with FindInstance

How to find individual root parameters pair ( t, T) to find curve intersections using FindInstance? Hopefully it would output two, instead of 6 pairs in the following: ...