Questions tagged [equation-solving]

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

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128 views

Solve System of congruences

How can I solve a system of linear congruences as such? $$\begin{align*} 3x+2y+28z &= 9 \pmod {29} \\ 5x+27y+z &= 9 \pmod {29} \\ 2x+y+z &= 6 \pmod {29} \end{align*}$$ I tried it this ...
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3answers
146 views

Plotting the solutions of the equation $e^{-z}=z$ in the complex plane

I would like to plot in the complex plane the solutions of the equation $$e^{-z}=z.$$ I tried this: I took $z=a+ib$ and took the real and imaginary part of the equation: ...
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1answer
60 views

How to use NDsolve for PDE? [closed]

I am trying to use NDsolve to solve PDE which has an exact solution and evaluate the absolute error: ...
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1answer
43 views

No real solution for 3 coupled equations, but then how "close" can one get?

I have three equations involving $x$, $y$, and $z$ that I would like to find a unique solution to, in the Reals. NSolve does not find anything: ...
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1answer
76 views

NSolve syntax for region

I am trying to solve these simultaneous system of equations only in a specified rectangle going from -100<x<100 and -100<y<100. But I think I am making a syntax error and hence I m not ...
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2answers
59 views

Sum three equations [closed]

I would like to compute x1+x2-x3 based on three equations as defined in equations variable. See below: ...
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2answers
133 views

Any way to get Mathematica to Solve[Sin[Tan[x]]-Tan[Sin[x]]==0,x]?

Solve[Sin[Tan[x]] - Tan[Sin[x]] == 0, x] It says it runs out of methods. After a very long time. Plotting the expression shows there are periodic solutions and ...
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1answer
95 views

A No-linear differential equation

I'm recently figuring out how to make this equation solved but Mathematica does not solve this??!! DSolve[{ y'[t]== ((3 a)/2 (y[t] - b/(2 a))^2 + k ((3 a)/2 - 1) t^-2 - ((a f)/2 + (3 b^2)/(8 a)))/(t ...
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2answers
44 views

FindRoot with vector function

I have trouble with FindRoot for vector variables, I have search MMA SE find a solution. in Szabolcs‘s code, Vector FindRoot ...
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2answers
91 views

How to realize NDSolve by NSolve with the implicit constraint equations?

Daniel post the amazing code to realize numerical integrators, I think it is useful to the kind of one-step explicit equation like x[k+1]-x[k]== constant_number. In ...
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1answer
56 views

How to realize NDSolve by Solve?

I want realize the NDSolve by Solve,so I read some numerical integration resource. In common setting, ODEs can be solve by Euler ...
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0answers
35 views

Converting 1D map into first order differential equation for bifurcation diagram code

I have existing code to plot bifurcation diagram for coupled first order differential equations. It seems to work for coupled differential equations. To test the code further, I use the simplest ...
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3answers
168 views

How to use Findroot in a loop

Consider: i = 0.1; While[ i < 0.9, y[x_] := y /. FindRoot[{u/(1 - u) (x + Log[y]) - 1 /. u -> i}, {y, 3}]; Plot[y[x], {x, 0, 4}]; i = i + 0.1] I want ...
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0answers
43 views

How to fix a parameter in SolveAlways

In expression: SolveAlways[f1(a)+f2(b)x+f3(c)x^2+f4(d)x^3==f5(d)x^2+f6(e),x] Functions fi are known. How do I tell mathematica that d is a fixed constant?. I want ...
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2answers
148 views

FindMinimum::lstol

I have a function SQ[b,zQ,zh] where I want to find at which zQ it is a minimum given b and <...
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1answer
170 views

Why reduce does not give solution for ArcTan[Tan[x]] == x?

Basic question I can't see why now. This works Simplify[ArcTan[Tan[x]] == x, Assumptions -> -Pi/2 < x < Pi/2] (*True*) But ...
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0answers
51 views

Solving a 1D diffusion equation [duplicate]

I am new to Mathematica and I'm trying to find the analytical solution to the diffusion of excess pore pressure in a porous media using this equation: $$ \frac{\partial P}{\partial t} - \alpha \nabla^...
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3answers
46 views

NSolve not giving a solution

I have a parameter set paramFinal2 = {\[Beta] -> 0.2, \[Alpha] -> 0.5 , c -> 0.150, b -> 0.1, \[Kappa] -> 1}; I define the following variable ...
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0answers
47 views

Inverse VS Reduce

I got a solution I want to get inverse but it is not working in Mathematica or Rubi: ...
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1answer
46 views

"Instantiate" an output of Solve [closed]

I would like to use Mathematica to find a non-trivial solution of the linear system $Ax = 0$. When I try running Solve[A.x == 0, x] the output I receive is a ...
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1answer
39 views

Want a DiscretePlot of an NSolve that uses a parameter n

Let's say I want to solve f[n,R]==0 with respect to R for n=1,2,3,... (up to some upper ...
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0answers
32 views

please help me resolve find what method gives me a result for this

I have this mathematic problem: (124164a/300b/2360/.85)+(124164a/25b/2360/.85)+(124164a/55b/2360/.85)=3.81=(a/b/2360/.85) And this is the result: a≈87.4514, b≈0.0114422 I payed for WolframAlpha Pro ...
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1answer
43 views

Findroot to evaluated a function that become multivalued and varying of a parameter

I am having problem in solving this equation: s[t_?NumericQ, l_?NumericQ] :=FindRoot[s - Sin[t - (l*s)] == 0, {s, t, l}, Method -> "Automatic"][[1, 2]] ...
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0answers
94 views

Why does this ConditionalExpression appear? [closed]

I am new to Mathematica. Could anyone help explain why ws > 0 appears in the solution? How to define symbolic variables' range? Thanks! EDIT to include code <...
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0answers
64 views

FindMinimum/FindRoot failed to converge

I have a function SQ where it is also determined by sig. For b=0.1 and ...
2
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1answer
60 views

Strange behavior of NDSolve (Error NDSolve::ntdvdae)

i discovered a weird behavior using ```NDSolve``` to solve a set of differential equations. Let me outline my problem: I need to solve a set of differential equations. These are equations of motion ...
2
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2answers
299 views

How can I find the only real and then the smallest root of a 4th-order polynomial?

I just want to solve the below polynomial for real roots only, where I have mentioned the conditions on all variables, a,d,m,L. ...
2
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0answers
52 views

I need help with a basic Solve question

I have the following two conditions: Dc == t0^2 Dp == t1^2 The actual formulas I'm trying to solve are more complex, but this is the essence of the relations. I ...
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2answers
57 views

How to use NSolve while specifying the range of one variable

I have an equation that uses three variables that I have defined as follows: b[l_, m_, lt_] := 0.025 * (((1 - m)*l)^(-1/2))*((1 - m)*lt) - 5. After this definition, ...
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0answers
35 views

Different Outputs from Solve

These commands tell me that y=x^2 doesn't intersect the x-axis. But when I enter this slightly differently the intersection points appear. What's happening? This code tells me that y=x^2 doesn't ...
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1answer
55 views

LogicalExpand does not work correct?

I have a boolean expression and need to distribute all it's part. I used LogicalExpand and it works fine somehow. but I see for some sub-parts it does not Simpify or solve it. I tried Simplify for ...
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1answer
80 views

InverseFunction of ArcTanh and Log [closed]

I solved an equation and one solution was this: ...
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2answers
63 views

How to solve system of equations with complex variables

I'm trying to obtain the solution to the following system of 3 equations and 4 variables: ...
5
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1answer
129 views

What Does this Syntax Mean in Ouput from DSolve?

When I run the code DSolve[y*D[f[x, y, z], z] - z*D[f[x, y, z], y] == 0, f[x, y, z], {x, y, z}] I get the following output. I don't understand this syntax. I ...
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0answers
43 views

Reduce returning redundant solutions

When I call reduce on the following system: ...
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2answers
77 views

How to Plot an Equation, based on another plot [closed]

I've been struggling with this problem That I have an equation with two variables. One of them has a defined interval. Like this: ...
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2answers
104 views

Efficent ways to use NSolve, Reduce

hope you're having a nice day! Context: I'm trying to constrain parameters from a model of Orbital Resonance equilibrium. In short, I know a parameter "$\Delta_{eq}$" which is derived from ...
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0answers
52 views

Reduce does not work with Mod operation

We have a constant issue about working with some functions like Mod and Log. here when I add a ...
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1answer
194 views

Solving quadratic equations bug in Mathematica 12.3

There seems to be some sort of bug in mathematica, where sometimes it will treat a quadratic equation as a quartic equation. For example: ...
2
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1answer
38 views

What is the meaning of this Modulus output?

Quick question, what is the meaning of the $\mathbb{c}_1$ subscript in the output of Modulus (shown as an image below)? I understand there are two solutions to this linear congruence, 6 and 15 (6+9), ...
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0answers
44 views

problem in returning relations with unified format

first of all I didn't know what could be the proper title for this question, you may edit it if you find better, thanks. I am making some relations dynamically, relations will return based on two type ...
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0answers
29 views

Reduce for non-linear NSolve for Elliptic functions

How to Reduce in DSolve of the non-linear equation arising from inverse Elliptic functions? Thanks for all help, there seems no standard way to deal with it. ...
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2answers
143 views

Showing that a Hopf bifurcation exists?

I have the following system of ODEs: dx/dt = a/(1 + z) - Q*z dy/dt = Qx - qy dz/dt = qy - cz/(K + z). Assuming K = 1, Q = q < c, and a = c*(Sqrt[c/Q] - 1), is there a way to use Mathematica to test ...
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1answer
125 views

How to find an instance of this inequality?

I am trying to show that a given inequality is true for some triple but I am having trouble finding anything. Here is a tiny version of what I am working with: We define the following polynomials <...
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1answer
65 views

How to plot using ListPlot and FindRoot

I am new to Mathematica, now I have an expression Implicit\[Omega]Zero with some parameters $\lambda1,\mu rr,\theta s,b0,a,b1,\omega$ Now I want to find the $\omega(...
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0answers
85 views

Non linear first DE with lot of parts

I want to know how I can solve this equation in Mathematica I guess I missed something!! DSolve[ {a (h[a])^2 h'[a] +(nh[a]/ a^2) + m(h[a])^3 - l (h[a])^2 - t == 0}, h, a] h[a] is my function and n,m,l,...
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1answer
105 views

How to solve that logarithmic equation? [closed]

I mean an equation $$ \log _{2 \sqrt{\sqrt{3}+2}}\left(x^2-2 x-2\right)=\log _{\sqrt{3}+2}\left(x^2-2 x-3\right).$$ The result of ...
2
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1answer
136 views

How to expand a function as a linear combination of other functions?

I would like to be able to expand certain functions as linear combinations of other specified functions when I know that the original function can be represented in such a way e.g. we know that $\sin^{...