Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
4,078
questions
0
votes
1answer
75 views
How can I simplify my geometric calculation?
Here is a math problem I am dealing with right now:
Given ellipse $C$: $x^2/a^2 + y^2/b^2=1$ ($a>b>0$). Ellipse $C$ passes through the point $P$: $(1,3/2)$, and has eccentricity $e=1/2$. ...
3
votes
1answer
60 views
0
votes
1answer
65 views
Obtaining a parameter using Brent's method
Using Brent' method, I want to find a $g$ which minimizes $\Delta$ that is defined as
$$\Delta=\sum_{n=1}^N F^2_n \tag{1}$$ where $F_n$ is $$ n(n-1)\mu_{n-1}+2Z\mu+2E\mu_{n+1}-2\alpha\mu_{n+2}-2\beta\...
7
votes
2answers
87 views
1DPoisson equation with Dirac delta
I was writing my own FEM method to solve the Poisson equation
\begin{align}
-u'' &= \exp(-c(x-1/2)^2)\\
u(0) &= u(1) = 0
\end{align}
where c=100.
and I'm reading from the book of Mats G. ...
0
votes
0answers
36 views
Solving a large linear system
I have a system of 12 equations with very large symbolic expressions but linear in some variables that I want to solve it for. I have been running Solve for many ...
0
votes
1answer
76 views
Solving a well known transcendental equation [on hold]
Evaluating
Solve[E^(n t) == Cos[t] + n Sin[t], n]
does not produce a solution for $n$. What method should be used to solve for the value of $n$?
-2
votes
1answer
41 views
0
votes
1answer
39 views
Solve returns complicated and wrong solution
I have the following equation
(8 F (D1 + ((D2 - D1) nf)/n)^3)/(G d^4) == H/n
Solving for $n_f$ by hand is simple and gives
$$
n_f=\frac{n}{\text{D2}-\text{D1}} \...
0
votes
1answer
38 views
points of intersection along curve and horizontal line [duplicate]
I'm trying to find the intersection points of the following plot with the given boundaries. How would I do so in the bounds set by the above plot? I've tried FindRoot by setting the lines equal to ...
1
vote
1answer
54 views
NSolve for x and y
I'm trying to solve the following for x and y, but the evaluated cell just gives me back what I tried to solve, just a little more simplified.
If both x and y were bounded from [0,5], how would I ...
0
votes
2answers
61 views
Find best fitted approximated parameters
I want to find the best fitted approximated parameters for the following case:
$$\begin{align*}
2a + 3b &= 5\\
a + b &= 4\\
a + b &= 3.9\\
2a + 3b &= 5.1
\end{align*}$$
When I use
<...
1
vote
1answer
45 views
solve equation by explain n*n matrix or equation team
I want to solve n equation which has n root with Gauss-Elimination Method. I indicated root formulation and methodology in picture. But I don't know that how can I do this. Should I explain n*n matrix?...
-4
votes
3answers
84 views
How to print by using For loop? [on hold]
For[mu = 0; mu < 6, mu++,
mu = -4.84*10^(-4) - 17.82*10^(-4)*T1 +
1.53*10^(-4)*T1*2.303*Log[T1]; Print[T1]]
I want to get the value of ...
2
votes
0answers
39 views
Never terminating when solving linear Diophantine systems
Say I have:
$(1):$ Set of Diophantine systems where each defines a (possibly unbounded) polyhedron.
This is solvable with existing algorithms:
$(*):$ The $(1)$ can be solved in SageMath with ...
0
votes
0answers
37 views
How robust are mathematica‘s equation-solving capabilities? [on hold]
My question regards using the Mathematica command as part of a rigorous proof. Rather than describe the general situation—- suppose I can the proof of a result to the fact a pair of equations $h(a,b)=...
0
votes
0answers
33 views
Is there a feasible computation?
I have to find the values of $p_1$ and $p_2$ which minimizes the expression $G$. However, when I took the partial differentiation of $G$ with respect to $p_1$ and $p_2$, the equations I obtained were ...
1
vote
4answers
94 views
Unable to find root for user-defined function
I created the function getSolution[xVal,yVal] for a geometry problem I'm working on and wish to solve it for getSolution[2,x]==0. I can plot it clearly showing the roots:
However, when I attempt to ...
2
votes
3answers
147 views
Mathematica Fails to Solve a System of 3 Equations!
I'm trying to solve what I thought would be a simple set of 3 equations for Mathematica! But it grinds endlessly without any result..
...
0
votes
0answers
22 views
NIntegrate in FindRoot: s=S is not a valid limit of integration
I get an error code saying that "s=S is not a valid limit of integration" when I use the following code:
...
2
votes
1answer
39 views
How to find the distances between two adjacent maxima in a solution from NDSolve
I try to find a general approach to plot the time evolution of horizontal distances from maximum to maximum in a solution of PDE. The solution u[x,t] normally have ...
0
votes
0answers
112 views
Need help with ParametricNDSolveValue for ODE with two variables and Do-loop
I' m trying to solve a tricky 2-nd order ODE with
ParametricNDSolveValue for boundary conditions (BCs) y = 0 at R and ...
0
votes
2answers
48 views
how to solve the equation
I want to sole the given equation for x. Can anyone help me please to analyse the solution. Thanks
...
2
votes
3answers
99 views
Solving 5 nonlinear equations, is there a suitable way?
I'm trying to solve a set of 5 nonlinear equations using NSolve:
...
0
votes
1answer
31 views
1
vote
1answer
47 views
Need help with ContourPlot3D
I need to print out the value of x, y, and z when h==0, g==0. Help please?
...
1
vote
1answer
90 views
Solve giving solution when there is no solution
I got a strange result from Solve.
I have the following relations:
...
0
votes
0answers
34 views
Getting an analytical form $f(x,y)$ from numerical solutions of a ContourPlot
I numerically solved a set of equations which yields a solution of the form $f(x,y)=c$.
I was hoping to obtain an analytic expression for $f(x,y)=1$ (in my case $c=1$) but all I managed to do was to ...
3
votes
1answer
113 views
Solve a one dimensional heat transfer problem with NDSolve
The following problem is a 1-D heat transfer conduction problem:
where,
I am trying to solve with NDSolve like this way:
...
0
votes
1answer
47 views
How to ask Mathematica to express variables in terms of each other in an implicit function
How to ask Mathematica to give $y$ in terms of $x$ in this function? Is there a way to obtain a closed form expression for $y$ in terms of $x$?
$x=\frac{\left(y^4-1\right) \left(\coth (2 y)-\frac{1}{...
3
votes
0answers
57 views
Why does FindInstance take so long: It is faster with more restrictions than with less?
A support case with the identification [CASE:4347836] was created.
I just noted this little puzzle on twitter by Brillant.org:
\begin{align} A B C\\+ BCA\\ = CDE \end{align}
Given that $A$ is even ...
14
votes
2answers
304 views
Convert symbolic to numeric code: speed up morphing
Recently I asked a question about the morphing between two functions and got two excellent answers. The accepted answer is using the continuous optimal transport theory. This seems to be very suitable ...
0
votes
0answers
27 views
Simulating a function with no closed form solution
So I am trying to simulate a function in 3d. Suppose our function looks like this:
f=k*r*a
I am interested in simulating the numerical values of k when r is ...
1
vote
2answers
35 views
Manipulation replacements rules from Solve [closed]
Assume the call to the routine Solve[eqn==0,{x1,x2}] returns:
{{x1->a1,x2->a2},{x1->b1,x2->b2}}
I would like to ...
0
votes
2answers
79 views
Verifying that a functions attends values below something
After plotting the graph of $$f(x)=\frac{π}{3\sqrt{2 π}} (\frac{e^{\frac{-x^2}{18}}}{3} + \frac{e^{\frac{-(x - 5)^2}{2}}}{1} +\frac{e^{\frac{-(x - 15)^2}{8}}}{2}
) (1 + x^2)$$
I would like to ...
0
votes
0answers
41 views
Solving an equation: Reduce command produces failure message
I am trying to solve the following equation for c:
All variables can only take positive values and c>s. I have tried the following code:
...
2
votes
0answers
28 views
Reduce[expr,vars] behavior when vars are not present
It is officially documented that Reduce should be used like Reduce[expr,vars]. However, I've used ...
0
votes
0answers
66 views
How do I solve a cubic equation for values of x?
I have partially differentiated an equation w.r.t. x, see picture below, and want to isolate x in the equation to solve for a local maximum.
Can I use Mathematica to get it on a cubic form? and how ...
2
votes
1answer
141 views
Why FindRoot does not give all roots? [closed]
I would like to solve complicated equation and use FindRoot to find roots numerically. I do not understand the following problem. I provide the simple example. Considert the equation:
...
1
vote
1answer
49 views
Hardy Ramanujan Question [duplicate]
I revised the code I asked about earlier, but I am still not getting an output. According to Mathematica it is (mostly) correct syntax. Here is the revised function:
...
2
votes
0answers
34 views
NMinimize with real solutions, problem in the resolution and criteria for other ways to solve equations
I have multiple parts in my question. You are welcome to answer to any of them :)
Part 1 :
I have 3 equations $p(x_1,y_1)=p(x_2,y_2),\mu_x(x_1,y_1)=\mu_x(x_2,y_2),\mu_y(x_1,y_1)=\mu_y(x_2,y_2)$. I'm ...
10
votes
1answer
286 views
Numerically solving a system of many coupled non-linear ODEs efficiently?
I'm studying a fairly typical problem: a chain of $n$ coupled, non-linear oscillators. Since I want to look at open boundary conditions, the equations of motion for the position of the first and the ...
3
votes
3answers
38 views
Using Element on list of numbers when defining equations
If been looking on how to construct equations with region or domains for some variables.
Suppose I have x and that x can only be the number 1,2,4 or 7
The equation 2 x < 10 will then results in x ...
0
votes
1answer
49 views
NDSolve for Complex Algebraic-Differential Equation
Let consider the following complex equations:
$$
\frac{i x(s)}{2\pi} - \frac{\log(1+ e^{-y(s)}) - \log(1 + e^{y(s)})}{\dot x(s)}
$$
which I will cal eq1 and
$$
\...
0
votes
1answer
70 views
How this equation is solved in reals
I have tried to solve this equation $2^{-2 ^{2^{-x}}}=2$ using
FindInstance[2^(-2^(2^(-x))) == 2, x, Reals]
The result is
...
2
votes
1answer
81 views
Efficient way to list zeroes of an oscillating function
From "The First 50 Million
Prime Numbers" by Don Zagier: primes are integral roots of$$
1-\frac{\sin(\frac{\pi\Gamma(s)}s)}{\sin(\frac\pi s)}.
$$
The graph of this function looks like
I would like to ...
0
votes
0answers
45 views
Roots of complex numbers
My exercise is to find $n$ roots of a rank $n$ of a complex number. Here is my code:
...
1
vote
1answer
54 views
Is priority important in `Series` expansion?
I have a strange case here! The story begins with this equation
...
3
votes
2answers
169 views
0
votes
2answers
70 views
How I can obtain u and z?
Integrate[1/Sqrt(2*Cosh[y] - 2*Cosh[u]) , {y, z, u}] == 0.013
2*Cosh[z] - 2*Cosh[u] == 0.41
Can I obtain the parameters of u and z using above equations?
3
votes
1answer
173 views
