# 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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### Maximizing a function that is only defined numerically

I have a function of multiple variables that is only defined numerically. I am trying to maximize the function and find the critical points as fucntions of two parameters p and s using FindRoot but I ...
43 views

### Speed up this computation involving NSolve many times?

Can you think of a way of speeding up this computation ? I don't. ...
43 views

### Plotting an integral with solving for a specific constant [closed]

Given an Integral I(t) which is a function of a constant tc, this constant is determined with the condition I(tc)=0, how can I add this condition?
1 vote
59 views

### Strange behavior of GroebnerBasis

Recently I tried to solve a multivariate quadratic equation over the reals, but with a parameter value. Since that took too long, I decided to try GroebnerBasis, ...
44 views

### How do I find roots of a third degree polynomial? [closed]

expr = G^2 X^3 - 2 Δ G X^2 + Δ^2 X + ((ℏ *G*η* k*Subscript[E, l]^2)/(m*Subscript[Ω, m]^2)) == 0
1 vote
70 views

### How to modify the order of symbols to make the result more logical [closed]

Simplify[(1 - a) (1 - b)] (-1 + a) (-1 + b) How to modify the order of symbols to make the result more logical. (1-a)(1-b)
144 views

### Solution of a sixth degree polynomial

I want to get the solution to a 6th degree polynomial in a certain range. I have the following code ...
105 views

### FindRoot with input as a list

I have three equations: eq1, eq2, eq3 with variables a,b,d,k. I wish to find the roots of these equations by assuming ...
77 views

### Adding Points on an Elliptic Curve

How do I do this in Mathematica? The curve given by the equation $y^2 = x^3 + 29x + 7$ defined over the integers modulo $10007$ Adding the first pair of points $P = (3737, 4549)$ and $Q = (8286, 6097)$...
240 views

### Getting all solutions to an equation on condition the variables are either 0 or 1

Given a list of 3-bit binary lists b={{0,0,0},{0,0,1},{0,1,0},{0,1,1},{1,0,0},{1,0,1},{1,1,0},{1,1,1}}; I would like to have all possible solutions to ...
1 vote
140 views

### Numerical solving diffusion equation in spherical coordinates

Mathematica nicely solves Poisson's equation in spherical coordinates as ...
1 vote
53 views

### First order differential equation with two conditions

I want to produce all possible solutions for this equation: ...
1 vote
62 views

### Problems with Solve. Only works for specific parameters. Solve function do not "start"

I have the following problem I want to solve the following equalities. My used code: ...
141 views

### How to solve this integral equation numerically?

I am encountering difficulties while trying to numerically solve an equation in Mathematica that involves an unknown function and an integral. Specifically, the equation takes the form of \begin{...
77 views

### Selecting Solve results according to conditions

When using the Solve function I get four possible answers. How can I automatically get the option in which x and y are positive? Where to insert the conditions x>=0 and y>=0? ...
1 vote
150 views

51 views

### How can i create an equation with a sum? [closed]

I have a list of $p_i$ and the condition that $\sum_{i=0}^{i=69} p_i = 1$ I also have a list of 69 other different equations. I want to use NSolve to solve for the ...
1 vote
99 views

126 views

### Solve[] isn't producing a correct result

I want to find the exact algebraic roots of the following function in terms of Z, P, Q, <...
56 views

### Is it possible to get rid of the square root in the solutions of the following symbolic quadratic equation?

I have a quadratic equation, which I want to solve, but don't want the square root to appear within the solutions. I tried converting the discriminant into a quadratic form but failed, not sure if ...
50 views

### How does Mathematica select principal roots of complex numbers?

When I do I^(1/3) I get Out[]:= (-1)^(1/6) which is one of the solutions of $z^3=i$. There are two more solutions which are ...
141 views

### Solving system of first order PDEs

I am trying to solve the 1st order PDE system \begin{align} \xi_u^2+\eta_u^2&= \left(1+\frac{\xi^2+\eta^2}{4} \right)^2\\ \xi_v^2+\eta_v^2&=\left(1+\frac{\xi^2+\eta^2}{4} \right)^2 \end{align} ...
45 views

### How to convert the equation into this two forms?

The equation is: x0^2/a^2 - y0^2/b^2 == 1 How to convert to this two forms: b^2 x0^2 - a^2 y0^2 -> a^2 b^2 and ...
1 vote
86 views

### Attempt to find a solution (out of potentially many) to a system of equations with FindInstance runs forever or crashes

I have a system of equations that in principle should have a solution (I would think not a unique one), which I want to solve. I am not interested in all solutions; I just want to locate one, assuming ...
1 vote
58 views

### Computing Displacement Potential functions

I am new to Mathematica. I am trying to compute the displacement Potential functions. My code is as follows. ...
56 views

1 vote
77 views

### Minimization of an implicitly specified function

exp - an experimental data, where expT - temperature, expChi - magnetic susceptibility I ...
1 vote
212 views

### How to simplify? [closed]

The original formula is: Abs[(a b)/x0]/(2 Sqrt[1 + y0^2/x0^2]) How do you convert operations to get this result? ...
85 views

### How can the process of hyperbola problems achieve the desired results?

As shown in the picture above, in the hyperbola x^2/a^2-y^2/b^2==1, point P is any point on the hyperbola, through the point P respectively do two asymptotes of the hyperbola parallel line PA, PB. The ...
103 views

### Calculate Bernoulli numbers ( with a twist) [closed]

Mathematica has an inbuilt function BernoulliB that calculates $B_n$ for which, $$\frac{t} {\left(e^t-1\right)}=\sum_{n=0}^{\infty} \frac{B_n}{n !}t^n$$ I need to ...
I have a function $c\cdot\frac{x^2}{x^2 + 10^{-6.367}*x + 10^{-6.367-10.32}} + x = c\cdot\frac{10^{-6.367-10.32}}{x^2 + 10^{-6.367}*x + 10^{-6.367-10.32}}+\frac{10^{-14}}{x}$, where \$0 < x < 10^{...