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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What class order should I use to study calculus?

I would like to know how I should go about studying calculus, and in what order should I take the classes. I have searched tirelessly for answers and I am still confused. Here is what I have gathered ...
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1answer
140 views

How can I find a functional square root in Mathematica?

A functional square root of a function $g$ is another function $f$ such that $g=f\circ f$. According to that article, there is a systematic approach to finding a functional square root that involves ...
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How to eliminate the list case by `Eliminate` function

It is known that line L1: $\frac{x-a_{2}}{a_{1}}=\frac{y-b_{2}}{b_{1}}=\frac{z-c_{2}}{c_{1}}$ and line L2: $\frac{x-a_{3}}{a_{2}}=\frac{y-b_{3}}{b_{2}}=\frac{z-c_{3}}{c_{2}}$ intersect at a point. Now ...
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1answer
34 views

How to define a function to decouple equations and transform them into standard form

I want to convert this expression($\frac{x-a 2}{a 1}=\frac{y-b 2}{b 1}=\frac{z-c 2}{c 1}$) of the linear equation into a standard form $\left\{\begin{matrix} \text { b1 } * x-a 1 * y=a 2 * b 1-a 1 * ...
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25 views

Reduce does not solve a 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 V3 as a function of the exogenous parameters. I am using the following code: <...
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42 views

How can I convert a list of rules into a list of equations? [closed]

How can I convert a list of solutions to a list of equations? For example, say I have: sol = {{a->1},{b->2}} and I would like to change it to ...
0
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1answer
52 views

Solve with > instead of == [duplicate]

I want to solve a complicated equation with the sign > instead of ==. However, mathematica Solve function is not defined for >. Can somebody tell me how to do it? Code example: ...
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30 views

Solve with Trig cycled variables

eqn={p2 == u^2 + v^2 - 2 u v csal, q2 == v^2 + w^2 - 2 v w csbt, r2 == w^2 + u^2 - 2 w u csgm} Solve[eqn, {u,v,w}] Hangs indefinite. How to Solve... using ...
3
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2answers
81 views

Solve system of equations with integration over regions

I want to solve the following problem in Mathematica: Assume that $\lambda_2=-\frac{1}{2}+ r+\frac{1}{1+r}- r^2\log\frac{1+r}{r}$, $v\in[0,1]$ and $\theta\in[0,1]$. For pre-specified values of $k,r>...
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56 views

Groebner Basis for Functions

We can use Reduce to solve the following Reduce[1 - Sqrt[a^(-1)] + Sqrt[2]*Sqrt[(a + a^2)^(-1)] - Sqrt[2 - 2/(1 + a)] == -1 + Sqrt[2], a, Reals] We can also do ...
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2answers
409 views

Why is Mathematica taking so long to solve this equation?

I was trying to solve a polarization problem where I needed to solve this transcendental equation. NSolve[(Cos[\[Pi]/n])^(2 n) == 0.90, n] I don't know why but ...
3
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1answer
74 views

Plotting in for loop

I am having some problem while plotting the data being generated in for loop My aim is to plot the result of for loop while it is solving the equation for each value of w,i.e. plot between w and x ...
6
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2answers
382 views

Finding the intersection(s) of a 3D parametric surface and a line

I have some 3D parametric curve par and some line line. I want to find parameters u,v and t for the intersection points of par and line. I tried to do that with NSolve in many different ways and ...
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2answers
139 views

Solve with inverse trig functions (4-Bar Linkage)

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1answer
61 views

How o use singular value decomposition function to find the natural frequency and mode shapes

I have a matrix R which is having a dependency on ω, I am interested in finding the natural frequency and mode shapes of this matrix using SVD how to do this?. The regular way is to take the ...
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2answers
150 views

How to solve a nonlinear second order ODE

I want to solve this equation y''[x] + a + b y[x] + c y[x]^2 == 0, y[∞] == 0, y'[∞] == 0 where a, ...
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1answer
108 views

How to solve a differential equation involving LaplaceTransform?

currently I'm working on a problem in which I need to solve an equation of the following form: $$\mathcal{L}\left[\frac{\partial f(x,t) }{\partial x} + \frac{\partial f(x,t)}{\partial t}\right] = \...
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33 views

Exiting CrossSlidingDiscontinuity in NDSolve to follow equilibrium curve

I am trying to figure out how to get the solution curve to an NDSolve to slide along once it reaches a boundary and then to exit the ...
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41 views

Solving a cubic equation in mathematica

I am trying to solve a cubic equation using Mathematica of a rather complicated expression say $f(r,\beta,\theta)$ , and in terms of $r$ the maximum degree term that appears is of degree $3$ so I ...
2
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2answers
114 views

How to solve Nonlinear coupled ODEs using DSolve

I cannot solve such a system of coupled ODEs in MMA 12.1 using DSolve. i.e. output is equal to the input equations ... (see the attached figure) Here, each solution is labeled according to the name of ...
1
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1answer
48 views

Says that my variable is 45 degrees and not valid [closed]

I tried to run Solve[2x+1==6,x] and it has given me an error saying 45 degrees is not a valid variable. How do I fix this?
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1answer
69 views

How to fix the Y-axis and normalize density?

I want to plot a density curve but when I draw the y-axis not getting to 1 (as normalized) ...
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1answer
57 views

How to do Interpolation to this function after given b this values

\[Chi][b_] := (Z/k)*NIntegrate[Subscript[f, pp1][q]*Subscript[F, pp1][q]*BesselJ[0, q*b]*q, {q, 0, b}]; bList = Table[b, {b, 0, 5.1 , 0.05}] where: Z = 6; k=1....
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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
112 views

Solve a system of differential equations

How to solve this system of equations?
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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): ...
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51 views

Help me factor this equation

I have the following equation: $$\frac{2\left(a A_3 r + \frac{1}{2} r^2 a'^2 \right)}{a^2 r^2}=\frac{8 G \pi \rho}{3}-\frac{c^2 k}{a^2}$$ ...
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1answer
139 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
81 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
54 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 ...
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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
88 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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38 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 ...
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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
153 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 ...
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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] ...
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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
30 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
52 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 ...

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