# Tag Info

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 ...
• 18.6k

### How many solutions does this system have?

We can try FindRoot as follows ...
• 45k

### How many solutions does this system have?

Try ContourPlot and MeshFunctions in order to estimate numerically the number of solutions: ...
• 54.1k

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

You can use AsymptoticSolve for this purpose: ...
• 131k

### Coupled pdes with two different derivatives

First equation can be integrated alone, as result we have for ux=D[u[x,t],x] ...
• 45k
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 ...
• 12.6k

### 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 ...
• 74.2k

### 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, ...
• 41.5k
Accepted

### Solving a first order linear matrix differential equation

Write the matrix elementwise then it will work: ...
• 52.6k

### 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 ...
• 18.6k
1 vote

### Solving equation analytically

An exact solution, better than the approximation you give, is ...
• 47.9k

### Solving equation analytically

If you want only approximation use: AsymptoticSolve, because exact analytical solution can't be found. ...
• 13.9k

### 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: ...
• 47.9k

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• 159k
Accepted

### Plotting Phase Portrait of Duffing Equation

The best what we can do with StreamPlot ...
• 45k

### 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 (...
• 3,772

### 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) ...
• 74.2k

### Plotting Phase Portrait of Duffing Equation

Using ParametricNDSolve with {a,b} be the initial point. We solve {U,U'} simultaneously( see ...
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• 456

### 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): ...
• 47.9k
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 ...
• 47.9k

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• 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 ...
• 111
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: ...
• 236k

### 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 ...
• 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. ...
• 3,772
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 ...
• 61.6k
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 ...
• 61.6k

### 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]
• 2,850

### 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 ...
• 636
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 âˆˆ PositiveIntegers, x] gives ...
• 145k
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• 159k

### 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 ...
• 14.5k
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. ...
• 145k

### Solving Diophantine equations

A general expression can be obtained using Reduce. Because this function seems to prefer working with polynomials, replace z in ...
• 61.6k

### 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 ...
• 52.6k
Accepted

### How to divide a known root out of a polynomial?

PolynomialQuotient is enough. I just used PolynomialQuotientRemainder to see that remainder is indeed ...
• 18.6k

### 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). ...
• 57.5k

### 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: ...
• 61.5k
Accepted

• 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 ...
• 45k

### 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]
• 61.5k

### 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 *)
• 4,604

### 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 ...
• 59.1k

### Why does this system of trigonometric equations have no solution?

Just a variant of @BobHanlon excellent answer illustrating there is no solution: ...
• 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 ...
• 55.4k
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 ...
• 145k
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• 159k
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• 159k