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1 vote

How many solutions does this system have?

This is a exact and "error/warning-messages-free" method. Firstly, there are roots that can be expressed exactly as ...
azerbajdzan's user avatar
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3 votes

How many solutions does this system have?

We can try FindRoot as follows ...
Alex Trounev's user avatar
4 votes

How many solutions does this system have?

Try ContourPlot and MeshFunctions in order to estimate numerically the number of solutions: ...
Ulrich Neumann's user avatar
2 votes

How to invert a series with two variables, where the series is expanded in the other variable?

You can use AsymptoticSolve for this purpose: ...
Carl Woll's user avatar
  • 131k
0 votes

Coupled pdes with two different derivatives

First equation can be integrated alone, as result we have for ux=D[u[x,t],x] ...
Alex Trounev's user avatar
1 vote

A first order differential equation: Inconsistent solutions by two approaches

In both Wolfram Language 13.3.0 Engine for Linux and the cloud version 14.0.0, the original code produces the error message "DSolve::nolist: List encountered within ... There should be no lists ...
LouisB's user avatar
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3 votes

How can I select element of a list containing (a,b) where both a and b ara rational numbers and not integers?

list = { {{x -> -1}, {x -> 3}}, {{x -> -1}, {x -> -(1/2)}}, {{x -> -Sqrt[2]}, {x -> Sqrt[ 2]}}, {{x -> 1/3}, {x -> 1/2}}} A variant ...
eldo's user avatar
  • 74.2k
0 votes

How does FindRoot work?

One technique is to use Groebner bases--the analogy of Gaussian elimination in linear systems--to make an equation in x (solve that), use that in the second equation (in x and y)... solve that for y, ...
David G. Stork's user avatar
3 votes
Accepted

Solving a first order linear matrix differential equation

Write the matrix elementwise then it will work: ...
Daniel Huber's user avatar
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3 votes

Vortex beam profile plot

The spiral "gaps" are not the same for l=1 and l=2 they just look so because Alex Trounev used in his code ...
azerbajdzan's user avatar
  • 18.6k
1 vote

Solving equation analytically

An exact solution, better than the approximation you give, is ...
Roman's user avatar
  • 47.9k
0 votes

Solving equation analytically

If you want only approximation use: AsymptoticSolve, because exact analytical solution can't be found. ...
Mariusz Iwaniuk's user avatar
4 votes

Solving equation analytically

f[r_] = 1 - (2*M*r^2)/(r^3 + g^3) + (8/3)*Pi*P*r^2; v[r_] = f[r]/r^2; Let's substitute $\rho=r/M$ and $\gamma=g/M$ to simplify the equation: ...
Roman's user avatar
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0 votes

How to get the value of expression if I have some equalities?

...
Bob Hanlon's user avatar
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5 votes
Accepted

Plotting Phase Portrait of Duffing Equation

The best what we can do with StreamPlot ...
Alex Trounev's user avatar
0 votes

Solving equation analytically

For me res= ( Collect[(D[v[r], r] // Together // Numerator // FullSimplify), r] -2 g^6 - 4 g^3 r^3 + 6 M r^5 - 2 r^6 Inserting your (...
Roland F's user avatar
  • 3,772
2 votes

What is an easy way to transform an equality into a replacement rule?

eqns = (a == 1 && b == 2 && c == 0); Using MapApply (new in 13.1) ...
eldo's user avatar
  • 74.2k
6 votes

Plotting Phase Portrait of Duffing Equation

Using ParametricNDSolve with {a,b} be the initial point. We solve {U,U'} simultaneously( see ...
cvgmt's user avatar
  • 74.8k
0 votes

I can't get NSolve to work

...
Dotman's user avatar
  • 456
3 votes

How to find the solutions to $a+b+c+d=60$?

As of Version 13.2, Solve and SolveValues can do this directly (19871 solutions): ...
Roman's user avatar
  • 47.9k
6 votes
Accepted

How to find the Proportion?

a = 2 k; b = 3 k; c = 4 k; f = {a + b, b + c, c + a} (* {5 k, 7 k, 6 k} *) f / (PolynomialGCD @@ f) (* {5, 7, 6} *) The same thing but expressed in a ...
Roman's user avatar
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3 votes

I can't get NSolve to work

...
Bob Hanlon's user avatar
  • 159k
1 vote
Accepted

How to invert a series with two variables, where the series is expanded in the other variable?

I have found an answer using Solve. It's not a single function call as I'd hoped, but it could probably be made into a function. Perhaps other users will have ...
Christopher's user avatar
5 votes
Accepted

Is there any way to get DSolve to provide trivial solutions?

One way, but I'm sorry I don't have time to explain. Maybe after finals. Can delete if it's too obnoxious to have just code: ...
Michael E2's user avatar
  • 236k
2 votes

How to solve the integro - differential equation with complex value involved?

All three PDEs in the question have the form, {D[g[t, z], t] == Cos[t*z], g[0, z] == gz[z]}, where g is a function of ...
bbgodfrey's user avatar
  • 61.6k
1 vote

How to invert a series with two variables, where the series is expanded in the other variable?

By inversion polynomials of order 6 are involved, so computation is working numerical only, if the abstract root object representation has to be avoided. ...
Roland F's user avatar
  • 3,772
3 votes
Accepted

NDSolve fails first order ODEs, but works when transformed to second order

To illustrate my comment, obtain a formula for g'[R] from odes ...
bbgodfrey's user avatar
  • 61.6k
2 votes
Accepted

Why does singular solution not satisfy the ode?

This extended comment may help explain the situation. The right side of ode has a branch cut on the negative real axis of y due ...
bbgodfrey's user avatar
  • 61.6k
0 votes

How can I find values of m so that the function $\frac{-m+x^2+x-4}{4 x-m}$ increasing in the interval $(1,2)$?

Simple direct solution: Resolve @ ForAll[x, 1 <= x <= 2, D[(x + x^2 - 4 - m)/(4x - m), x] > 0]
TheDoctor's user avatar
  • 2,850
2 votes

How to solve an overdetermined system in Mathematica

A simpler solution than the proposed answers is to use the (apparently undocumented) third argument of Solve to specify the variables one wants to eliminate (see ...
divenex's user avatar
  • 636
3 votes
Accepted

How can I solve this inequation over positive integers?

Help it a little Reduce[2023^x + 2023^(101 - x)*(-1)^x < 0 && x < 100 && x ∈ PositiveIntegers, x] gives ...
Nasser's user avatar
  • 145k
2 votes
Accepted

NIntegrate inside FindRoot has evaluated to non-numerical values

...
Bob Hanlon's user avatar
  • 159k
2 votes

Plotting 3x3 Linear System

There is nothing wrong with your code as far as I can tell. You may think there is something wrong because the outputs look different. I believe this is because the orientation and scale of the three ...
Jack LaVigne's user avatar
  • 14.5k
3 votes
Accepted

Plotting 3x3 Linear System

Just due to display/plot/scaling difference. This gets to look almost the same by playing with plot range and Mesh options. ...
Nasser's user avatar
  • 145k
0 votes

Solving Diophantine equations

A general expression can be obtained using Reduce. Because this function seems to prefer working with polynomials, replace z in ...
bbgodfrey's user avatar
  • 61.6k
3 votes

How to divide a known root out of a polynomial?

FindInstance returns a rule, not a number. Therefore you need: root = x /. FindInstance[pol == 0, x][[1]] 1/2 (-1 - I Sqrt[3]) To divide the polynomial by the ...
Daniel Huber's user avatar
  • 52.6k
3 votes
Accepted

How to divide a known root out of a polynomial?

PolynomialQuotient is enough. I just used PolynomialQuotientRemainder to see that remainder is indeed ...
azerbajdzan's user avatar
  • 18.6k
6 votes

How to get the analytical form of a solution to an algebraic equation?

The simplest approach relies on observation that our polynomial $x^5 + 10 x^3 + 20 x -4$ is of the fifth order with integer coefficients divisible by $2$ (beside one with the highest order power). ...
Artes's user avatar
  • 57.5k
3 votes

How to get the analytical form of a solution to an algebraic equation?

Here is a way to do the manipulations in Mathematica/Wolfram Language: ...
ubpdqn's user avatar
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7 votes
Accepted

How to get the analytical form of a solution to an algebraic equation?

Using answer in Solving quintic in radicals QuinticToRadicals[sol[[1]]] gives Full code (see post above) ...
Nasser's user avatar
  • 145k
1 vote

Solving coupled quasi-linear PDEs with boundary conditions

We can solve this problem using FDM code from here with a small modification ...
Alex Trounev's user avatar
2 votes

Solution of $x=0$ for $\frac{4 x^2 (5 + x)}{20 x + 4 x^2} = 2 x$?

Here is some justification for MMA answer: a=(4 x^2 (5 + x))/(20 x + 4 x^2); Limit[a, x->0] Plot[{a,2x},{x,-1,1}] Solve[a==2x,x]
ubpdqn's user avatar
  • 61.5k
3 votes

Solution of $x=0$ for $\frac{4 x^2 (5 + x)}{20 x + 4 x^2} = 2 x$?

Mathematica 14 does the same. It looks like it is simplified first, so it solves x == 2x for x. (4 x^2 (5 + x))/(20 x + 4 x^2) // Simplify (* x *)
David Keith's user avatar
  • 4,604
0 votes

Ordering of solutions of NSolve

One way to go at this is to determine where these root functions cross. That can be done by finding zeros of the discriminant polynomial. For that we first need to get a polynomial. I use exact values ...
Daniel Lichtblau's user avatar
2 votes

Why does this system of trigonometric equations have no solution?

Just a variant of @BobHanlon excellent answer illustrating there is no solution: ...
ubpdqn's user avatar
  • 61.5k
1 vote

How to convert the form of the Solve solution to the form of the Reduce solution

One way could be: sol = {tanx -> 1/Sqrt[2], tanx -> -Sqrt[2]} Or @@ Equal @@@ List @@@ sol or ...
Syed's user avatar
  • 55.4k
3 votes
Accepted

How to convert the form of the Solve solution to the form of the Reduce solution

You can do it in 2 steps. First replace Rule by == and then change the head to Or ...
Nasser's user avatar
  • 145k
5 votes
Accepted

Why does this system of trigonometric equations have no solution?

...
Bob Hanlon's user avatar
  • 159k
2 votes
Accepted

Ordering of solutions of NSolve

...
Bob Hanlon's user avatar
  • 159k
2 votes

How to get the intersection between circle and rectangle?

Extending the answer by @Fidel, ...
Syed's user avatar
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