# Tagged Questions

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

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### Solving biharmonic equation with Mathematica

I would like to solve a biharmonic equation in polar coordinates of the form: $\Delta \Delta \Phi[r,\theta] = r^i cos(j \, \theta) \quad i,j \, \epsilon \, \mathbb{N}_0$ I know that a solution for ...
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### Solving a non-linear equation [duplicate]

I have one non linear equation, and I am trying to get value of x but when i employ Solve function as below ...
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### Issue finding roots in a polynomial [closed]

I am trying to find the roots of the polynomial (-2 + x)^3 (-2 + x^2) (-4 + x^3) (4 + 2 x^2 + x^4) (-8 - 8 x - 2 x^2 + x^3 + x^4) . I am using the command ...
321 views

### How to solve an equation with a nested function

I have the equation f[f[x]] == 28 + 9 x How can I solve this for f[x]? I note that this post relates to the topic, but ...
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### Solving an equation entered by the user via the Input function

I am new to Mathematica. I am trying to create a program that takes in an equation from user input and then gives the answer. I started with a manipulate function as I created a similar program for ...
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### Plotting the results from Solve in a Manipulate expression

I am a self-taught Mathematica user, trying to make some progress. This is my code: ...
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### Find smallest solution in Solve's solution set

When an equation has multiple solutions, how do you find the first solution? Example: Say we're trying to find the first positive x-intercept of the cosine function: $cos(x)=0 \land x \ge 0$ ...
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### Error In polynomial Root Finding

I have a polynomial in y like so: 2.00855*10^20 + 6.89796*10^20 x y + (5.17347*10^20 + 5.92241*10^20 x^2) y^2 - 1.4806*10^21 x y^3 + 7.77316*10^20 y^4 == 0 I ...
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### Solving equation containing ArcTan terms

IN MY EDIT I DESCRIBE HOW I GOT TO THAT EXPRESSION AND THE ORIGINAL PROBLEM. I have this expression: ...
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### Solve equations involving summation expressions in Mathematica

I am trying to solve the simple linear regression equation analytically in Mathematica (not using builtin functions). I managed to calculate the gradient as follows f is loss function using RSS and ...
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### Why is FindRoot failing to evaluate this function? [closed]

I have a (somewhat long) script which runs cleanly until the very last stage. Here, I'm using FindRoot to attempt to parameterize implicit curves in the zero set ...
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### Numerically parameterize portion of $F[x,y]==0$ [duplicate]

I have a relatively complicated function of two variables F[x,y] whose zero locus contains a number of intersecting paths in the $x,y$-plane. A problem I've been ...
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### Automation of Perturbation Solution

I'm trying to solve an equation of the form $$R(\theta)f(\theta)+hg(\theta) = 0$$ for small $h$, where $R$, $f$, and $g$ are functions. I've assumed a power series expansion for $\theta$ in terms ...
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### Reduce a complex inequality

Reduce[Abs[1/(1 + I/Sqrt[α])] < 0.5, {α}] It is taking long time to run. Can any one help me to get the reduced condition in terms of $\alpha$ or its modulus. ...
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### Using solve on conditional functions

I know that the code is pretty long, but most of it is just defintion. Do you see why the Solve gives me "his system cannot be solved with the methods available to Solve" back? ...
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Consider the two below ODEs with following dependent B.C. In the boundary conditions $k$ is an unknown. $$y_1''(x)=x$$ $$y_2''(y)=0$$ $$y_1(1)=y_2(1)$$ $$y_1(-k)=y_2(-k)$$ $$\frac{\text{dy}_1(1)}{\... 1answer 83 views ### Matrix equations solving can you explain me the easiest way for solving this matrix equation? I have this matrix: a={{-4,1,3,0},{-2,7,1,-1},{1,-1,9,-3},{-1,0,5,-10} and the Equation is: ... 1answer 89 views ### Precision of FindRoot Consider the following code: ... 0answers 66 views ### Avoiding divide by zero to simplify an expression enough to solve I have a very complicated expression that I'm trying to set to zero and solve. I simplify by substituting in variables, but Mathematica isn't fully simplifying it -- my guess is because it thinks it ... 1answer 72 views ### Solving a complex function in two parametres within a range Define: ... 2answers 39 views ### Stuck in Reduce and Findinstance function for the following problem ... 0answers 63 views ### Why can't Mathematica solve this complex equation? So I want to find the complex part of Rthev,equate it to zero and solve for ω but it won't let me. Is it because it thinks ... 1answer 80 views ### How can I solve a set of equations with variables and eliminate a few variables at the same time? I just started learning Mathematica since I needed for my current research. I'm trying to solve a set of equations with different variables, eliminate a few variables in the set, and express one ... 2answers 87 views ### Determining the value at which a function becomes non-real or undefined If I have a function f(x) that I only know numerically and that returns a real value for some range of values -\infty < x \leq a and complex values for a < x < \infty, how can I ... 1answer 44 views ### Solve matrix equation for matrix Is there any function like Solve but designed to deal with matrix equations? Something like: ... 1answer 105 views ### Evaluate an integral with parameters I already asked this on stack overflow but was redirected here. I am trying to solve the (highly non-linear) following system of equations : with and g_0, \Lambda are positive constants ... 0answers 40 views ### What is the default method used by NSolve I have a system of 6 polynomial equations of the form aijk xi xj + bik xi = ck (k=1,2,...,6; summation convention on i & j) I am using NSolve[{eq1,eq2,...,eq6},{x1,x2,...,x6},Reals] What ... 2answers 71 views ### solve system including piecewise function I've read posts about how to do this in a direct way, but the method doesn't work for my simple system? -- see code: ... 1answer 55 views ### function definition,  symbol apparition after variables [closed] I have a proble with a system of two differential equations ... 2answers 38 views ### How to solve equations involving binomial and summation expressions Mathematica is taking forever to solve the following equation. Is there any other way t solve this equation for x? ... 1answer 40 views ### Determine parameter from which on there is no more root for a given function Let \gamma>0 be a real number and \Phi(r)=\frac{1}{r}-\frac{\pi}{4}\left(H_0(r/2)-Y_0(r/2)\right) defined on [0,\infty), where H_0 is the Struve function of order zero and Y_0 is the ... 1answer 86 views ### Way to simplify an inequality with many variables my problem is the following: I have three inequalities in five variables x,u,a,b,c\in \mathbb{R},x>0 : ... 1answer 64 views ### Do not understand the result I'm getting from Solve [closed] I did Solve[k2 Cos[x] - k1 Sin[x] == 0,x] Since tangent is sin over cos, the solution must be arctan(k2/k1) But ... 1answer 52 views ### How to solve an iterative integral equation for a function in Mathematica 8.0? I would like to solve the following iterative integral equation in order to find the functional form of P_{0}(k) numerically and then use it subsequently for the rest of my code: ... 0answers 49 views ### diophantine linear equation with condition on the sum of coefficients [closed] I am trying to solve the following diophantine equation x*a + y*b == c where a,b,c are integers and the absolute value of their sums is, for instance, 4. Then I ... 1answer 31 views ### FindRoot outputs a lot of nlum and ReplaceAll errors before outputting (close) root I'm trying to find the root of the root function when some other variable is subtracted. I.e. FindRoot[root[theta, r, h]-H, theta] Whenever I do this, FindRoot ... 1answer 44 views ### Evaluating Root forms in a Table [closed] When I put a Root form in table, the parameters of the Root form don't evaluate. I don't know how I can indexed values substituted into root form in the table to get have numeric output. ... 2answers 135 views ### Solving system of equations with (nested) Bessel Functions I'm trying to find solutions to a system of equations which include Bessel functions. It feels like the problem for mathematica is that the arguments of the Bessel functions are functions themselves ... 1answer 71 views ### Nonlinear Markov chain (numerical simulation) Suppose you have a linear Markov process, and you can write it as x(t+1) = Ax(t). Here x is the vector of values, and A is the transition matrix. Since this is linear, it can be solved analytically, ... 1answer 132 views ### Undershoot/Overshoot Method for this differential equation? I have tried to solve this equation for some weeks and I am not capable. I have read in articles that it is easy with an undershoot/overshoot method, but I don't know how to do it. y''+\frac{3}{x}y'-... 0answers 86 views ### Solve equations with Monte Carlo [closed] I am dealing with a complicated problem. I will use a simple problem to explain it. I have two variables x and y, and two equations: x+y=A 2x+y=B The value of A and B is determined by measurement, ... 2answers 166 views ### Solving Boolean equations @Artes suggested this code to me to solve this system of equations: ... 1answer 85 views ### Solving and Plotting Infinite sums over solutions to transcendental equation involving Bessel functions I am trying to use Mathematica to plot the following equation E(q,\Delta) vs qa, for set values of  D \Delta/a^2 and \bar\rho a/D. I have looked at other stackexchange posts which deal with ... 1answer 68 views ### Stopping NDSolve when encountering stiffness I am solving a differential equation for different initial conditions using ParametricNDSolveValue. I need to look at the value of the solution at some later point, ... 1answer 44 views ### Probems using 2 For and a AppendTo to cycle through my Equation to solve some matrixes I am trying to solve a few problems here. I have an equation with multiple variables that I am trying to solve in For loop method. I will attach the file below. In addition I am trying to get it to ... 1answer 22 views ### build absolute value equations know solution [closed] We have absolute value equations with unknown coefficients: |x + a| = b and we know solutions: x = 11 and x = 5 We need ... 1answer 52 views ### Finding an Integer, Unimodular Matrix that connects two given matrices I have two symmetric, integer matrices, K and K_2 which have the same determinant and the same signature (number of positive - number of negative eigenvalues). I want to find an integer valued ... 1answer 59 views ### Solution of Coupled second-order ODEs and plot the diagram We have two second-order Coupled differential equations as the followings:$$\left\{\begin{array}{lr} \displaystyle \frac{{{d^2}{y_1}}}{{d{x^2}}} = \{ \frac{{\sqrt {\frac{{1 - {\varepsilon ^2}}}{{{{(...
I'm new to Mathematica, so my question may be quite trivial, but I need help. Let $F(x,y,a,b,c,d):\mathbb{R}^6\rightarrow \mathbb{R}$ be a function in 6 variables. I need to find conditions for $x$ ...