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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1answer
35 views

How to find the roots of a transcendental equation that depends on Bessel functions? [duplicate]

I am very new in wolfram mathematica, so i am having trouble in trying to find the roots for this transcendental equation. I am looking for roots of m. Acctually the first non zero value for m. Here J ...
2
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1answer
113 views

Solve a system of differential equations

How to solve this system of equations?
4
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1answer
227 views

How to solve the differential equation

I need to solve the differential equation DSolve[{(1-x)y''[x]==1/5 \[Sqrt](1+y'[x]^2),y[0]==0,y'[0]==0},y[x],x] but the result given seems to be incorrect and ...
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0answers
16 views

How to solve an equation by substituting possible solutions? [duplicate]

I wish to solve this equation for kappa, given a certain set of parameters (m and beta): ...
0
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0answers
51 views

Help me factor this equation

I have the following equation: $$\frac{2\left(a A_3 r + \frac{1}{2} r^2 a'^2 \right)}{a^2 r^2}=\frac{8 G \pi \rho}{3}-\frac{c^2 k}{a^2}$$ ...
1
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1answer
141 views

Implementation of the general solution of Abel differential equation of the second kind in Mathematica

Introduction An Abel equation of the second kind in its canonical form is writen as $$y(x)y'(x)-y(x)=f(x)\quad (6)$$ for arbitrary $f(x)$. Despite the fact that this equation has general solutions 1 ...
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1answer
91 views

Mathematica does not solve system of equations

I am trying to solve a system of 7 equations and 7 unknowns given a set of assuptions. I am only interested in obtaining V1 as a function of the exogenous parameters. I am using the following code: <...
1
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0answers
39 views

How to find solutions of a two-variable equation with discrete domains?

I have a two-variable function f[x_, y_] == 0, with a discrete domain for each variable, $x=\{1.5,\; 2.5,\; 3.5,\;4.5,\;5.5,\;\text{...},\infty \}$ and $y=\{0.1,\;...
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1answer
57 views

Root finding: Is there no bisection method root finder?

I am trying to find a root to an equation f[k,...]==0 numerically, where k is the variable I am solving for. Using both NSove as ...
0
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0answers
99 views

Is it possible to solve this equation analytically?

I have this equation, and I want to find an exact solution for $x$ in terms of $y$. I mean I want to obtain something like $x=f(y)$. Is it possible to solve this equation analytically by Mathematica? <...
2
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2answers
63 views

How to find non-trivial of a system of equation?

I have a system of four equations ...
5
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1answer
131 views

How can I reduce timing to solve this equation?

I am tring to solve equation $$\frac{2 \log (x y+2021)}{\log (2)}+4^{x+1}=2^{x y+2022}+\frac{2 \log (2 x+1)}{\log (2)},$$ where $x$, $y$ are integer numbers. I tried ...
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2answers
43 views

Evaluate with numbers from list

This code works: x=2 y/.Solve[y==x^2] Out[138]= 2 Out[139]= {4} So above I put number in variable x and getting the result of ...
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4answers
121 views

Is it possible to get a symbolic or numeric relation when solving a transcendental equation? [closed]

Here is the code. Solve[(1 - E^x + (3 x^2)/2)/(2 x) == a, x, Reals] Unfortunately, Mathematica told me that this system cannot be solved with the methods ...
2
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2answers
89 views

How can I solve $\coth (2 x )=x $? [duplicate]

I have this equation $$\coth (2 x )=x $$ and I want to solve it to find $x$. The methods Solve and Reduce do not work. Coth[2 x] == x
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0answers
39 views

How to deal with unknown variables in NSolve?

I am trying to solve these equations by using NSolve and want to plot $p1^{2}+p2^{2}$ v/s P0. But there is some problem, it is showing running... but not showing any error. I don't know where I am ...
1
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1answer
69 views

Why mathematica does not solve the equation $x\left \lfloor x \right \rfloor=10$ for $x$?

The equation $x\left \lfloor x \right \rfloor=10$ has a real solution, which is $x=\frac{10}{3}$. But when I type Solve[x*Floor[x] == 10, x] a message comes: "...
6
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1answer
167 views

How to solve system of PDE's with complicated initial and boundary conditions

I am trying to solve the Cavity problem given in Paper by Mansour et al. with a physical model . System of PDE and B.C are . How can I impose boundary conditions like this? Code ...
0
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1answer
38 views

how to solve a quadratic diophanic equation on integers and obtain various results

This quadratic di equation has more results, as it came to them. I can only think of this FindInstance[(4 p + 3 q - 2) (p - 1) == (6 p + 2 q) q, {p, q}, Integers] ...
1
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1answer
39 views

Find the condition under which an inequality holds

I've got an inequality of 8 non-negative parameters (arising from a 5x5 matrix) and would like to find a condition under which my inequality holds. The condition would be an inequality too of these ...
0
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1answer
32 views

why mathematica Holds the Solve on the set of equations in the diagonal a matrix?

Say I have a simple function F[x_, y_, z_, r_, a_, b_, c_, d_] := (1 - a + b - (b/3) (c x + d (y + z + r))) x And I want to solve the set of equations given by: <...
2
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1answer
53 views

Find non-unique Hermitian solution to pair of matrix equations

This is a continuation of my previous question here, but I previously did not fully specify some of the restrictions on the matrices and so the solutions posted there were not that helpful. I'm ...
3
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1answer
104 views

two tier compound interest problem

I am trying to make sense of how mortgage repayment figures are calculated for two tier mortgages, where you fix your interest rate for a certain period and after that period, you fall back to the SVR ...
1
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1answer
31 views

Get Solution range of NSolve

I have a numerical solution and when I solve it with NSolve, and substitue the results in an expression, I get something like: 1 + x + x^2 if 0 < x< 10 I ...
3
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1answer
75 views

Solving Inequalities using Mathematica

How can I solve this inequality using Mathematica? Sqrt[B^2 + J^2] Cosh[(2 J)/T ] < J Sinh[ (2 Sqrt[B^2 + J^2])/T] where T, J, and B are reals and they are >...
2
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3answers
80 views

How to solve these complex equations for plot?

I am trying to Plot this code but it is not showing any plot. I want a bistable type plot between "NL" and "P0" and there are six equations and six unknowns. The code is given ...
0
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1answer
52 views

Problem of Encountered non-numerical value for a derivative at t == 0

I try to solve this equation numerically : eq= z''[t] + (2691+ D[Log[Abs[z'[t]^2]],t]) (z'[t]^2 + Abs[z'[t]]^2 ) == 0; By ...
6
votes
3answers
148 views

Verify an inequality of many parameters

I've got an inequality of 10 non-negative parameters (arising from a 5x5 matrix) and would like to verify whether it holds. I tried the following, which doesn't seem to work: ...
2
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2answers
126 views

Underdetermined system of equations

Could anyone help me solve this probably simple equation? ...
1
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1answer
106 views

Solving symbolic system of non-linear equations takes too long

I am trying to solve a set of system of symbolic non-linear equations: ...
0
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1answer
41 views

How to solve all the solutions of this restricted system of equations?

The system of equations is as follows: ...
3
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1answer
98 views

Problem with NDSolveValue : “The function value {$Failed} is not a list of numbers with \ dimensions…”

I was having fun modifying a code given to me as an answer to a previous problem here, courtesy of user Alex Trounev (Thank you again), when I encountered a certain error which I had never seen before....
3
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2answers
160 views

Solving the Shifted Neutral Axis Problem

Problem Description: In solving the "Shifted Neutral Axis" method for the stress distribution of a vertical steel vessel supported on a concrete foundation, we can derive the following ...
3
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1answer
69 views

Solve an equation with real parameters

I am trying to solve $$ \left(\eta ^2-1\right) \cosh ^2(\beta \eta )+2 J^2=2 \eta (J \sinh (\beta \eta ) \sinh (\beta J)+\eta \cosh (\beta \eta ) \cosh (\beta J)) $$ for $\eta$. Where, $\beta, ...
2
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1answer
80 views

Converting an equation to the form $ax+by=c$

I have a linear equation that comes as a result of applying orthogonality on a non-homogeneous boundary condition with two unknowns $C_1$ and $C_2$. Can someone help me to express this equation in the ...
4
votes
1answer
56 views

Solve a linear sytem of differential equations (Cauchy problem)

I'm trying to solve a linear Cauchy problem (which should have a unique solution) as: $\dot{X}=Q^{11}X+Q^{12}Y,X(0)=I$ $\dot{Y}=Q^{21}X+Q^{22}Y,Y(0)=0$ The matrices $Q^{11}, Q^{12}, Q^{21}, Q^{22}$ ...
1
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1answer
51 views

Solve won't find solution to simultaneous matrix equations

I'm trying to solve a pair of simultaneous matrix equations of the form, $$AX + XA^\dagger + BJB^\dagger = 0,\ \ X C^\dagger + B J D^\dagger = 0,$$ where, $$J = \begin{bmatrix}1&0\\0&-1\end{...
0
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1answer
30 views

How to plot a Root[] object? [closed]

I got a solution in the form of a Root object from an equation: ...
4
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1answer
131 views

Simplifying the final coefficient expression of the solution to a Laplacian

I have been trying to solve a boundary value problem analytically which involves a three-dimensional temperature Laplacian over a parallelepiped. In the final step of my solution, using the two non-...
6
votes
4answers
145 views

Solve system of ODEs for steady state symbolically

I can successfully solve a linear system of ODEs describing chemical reactions by first using DSolveValue to find the general solution and then taking the limit to infinity to find the steady state ...
1
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1answer
83 views

Problem solving a function using FindRoot and then plotting it

When I run the following code: ...
1
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1answer
41 views

How to solve integral of second-degree exponential function?

I am trying to solve the internal of the second-degree exponential function. But Solve fails to give the solution. Is there any way to get the solution? By the way, I don't understand the ability ...
1
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1answer
79 views

How to solve complex equations and plot the graph?

I am trying to solve these equations and want to plot the value of $a^{\dagger}a$ versus P0. I have tried this code but this gives me an error like "Conjunction::argr: Conjunction called with 1 ...
4
votes
2answers
110 views

Re-writing $f(x, y)$ as $g(x)h(y)$ [duplicate]

Is there a general way of re-writing a function of two variables as a product of two functions, $$f(x, y) = g(x)h(y)$$ Specifically, I’m trying to write an expression, $$f(x, y) = \frac{a y - x}{y - 1}...
1
vote
1answer
51 views

Real Roots of Cubic equation [duplicate]

If I have the cubic equation, how can i find the real root of x ? I try this but i get complex root Solve[b (q - 1)*(x^3) + (m - s)*(x^2) + (a - n)*x + v == 0, x] ...
3
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1answer
102 views

Solve 2D Difference Equations

If I have a system of difference equations $$ \begin{cases} x(n + 1) = x(n) + x(n) y(n) + y(n)^2 \\ y(n + 1) = y(n) - x(n)^2 + y(n)^2 \end{cases}, \text{ with } \begin{cases} x(0) = 1\\ y(0) = 2 \end{...
2
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1answer
91 views

Solving a system of polynomial equations - can I be sure that the number of solutions, and the solutions are correct?

I need to solve a system of two polynomials with integer coefficients in two variables, $\{Q_1(w,z)=0,\,Q_2(w,z)=0\}$, and want to compute all real solutions. I'm able to run ...
3
votes
3answers
105 views

Find solution for specific similarity transformation

I have a situation where I need to find a similarity transformation of a specific form. I have some Hermitian matrix $X$, and I need to find a matrix $T$ that satisfies $X = T J T^\dagger$ where, $$ J ...
4
votes
3answers
73 views

Solving an equation for a space dependent variable

How can I find $f(x)$ in the interval $(x_1,x_2)$? I know the values of the coefficients as $c=0.5$, $b=1.1$ and $(x_1,x_2)=(-10,10)$. f[x] == c Cos[2 f[x]] + b x ...
0
votes
1answer
60 views

Counting real roots of bivariate polynomial

For a proof, I'm working with a polynomial $p(x,m)$ and I need to show that: For any $m\in (0,6)$, $p_m(x)\equiv p(x,m)$ has a unique real root in $(0,1/2)$. I find that this is true by using Reduce ...

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