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

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7
votes
3answers
356 views
1
vote
0answers
19 views

Solving a pair of recurrence relations [duplicate]

Why does this RSolve[{y[t] == a*y[t - 1]}, {y[t]}, t] work, while this ...
0
votes
1answer
105 views

Solving a system of two equations of third degree

I am trying to solve the following system of two equations for x and y. The solutions for x and y have to be positive and the parameters s and c are positive (to have a coherent interpretation of my ...
0
votes
1answer
114 views

Why mathematica have difficulty solving nonlinear equations? [closed]

I tried to solve this equation via Mathematica: ...
1
vote
1answer
99 views

Solution of Coupled Second Order ODEs with Boundary Conditions

D[Tu1[x], {x, 2}] qu - Tu1[x] (fu0 + I w p) == Tou[x] f1 D[T1[x], {x, 2}] q - T1[x] (f0 - b g0 + I w p)== To[x] (f1 - b g1) - g1 For T1 , ...
0
votes
1answer
78 views

Coefficient of function different than polynomial

My question arise from the problem that Mathematica can't solve the equation $$ \text{Solve}\left[e^{a-x} (0.0299584 a+0.1 b-0.0299584 x-0.152913)-0.9 a+0.9 b+0.9 x+0.18=0.0498614 e^{-x} \left(e^a ...
0
votes
0answers
32 views

FindRoot with units error: Message text not found

This is sort of embarrassing. I'm working on a document to extol the virtues of Mathematica, and I can't get it to solve a relatively simple system of equations involving units. In this code, when I ...
5
votes
2answers
1k views

Solving a trig equation

I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ? ...
1
vote
1answer
209 views

How do I get all possible solutions in an underdetermined system? [duplicate]

I have two problems which I'd like to solve with Mathematica. If I have a system of two equations with three unknowns, how can I get to list all possible solutions for the unknowns? Here is what I ...
3
votes
1answer
276 views

Solving a differential equation with initial conditions

I want to get a solution to an ordinary differential equation with imposed initial conditions. I'm confused about why my following code doesn't work: ...
10
votes
3answers
2k views

Solving a time-dependent Schroedinger equation

I want to solve the time-dependent Schroedinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t) $$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so ...
1
vote
1answer
113 views

Solution of an ODE in implicit form

For some non-linear ODEs there is only implicit form of solution using DSolve. For example DSolve[(y[x] + x - 1)*y'[x] - y[x] + 2 x + 3 == 0, y[x], x] gives ...
12
votes
3answers
502 views

How can I simulate this toggle mechanism?

I've been introduced to Mathematica very recently. Basically, I haven't actually "solved" anything in my Mathematica lifetime, but I've done some simulations. With my fractional knowledge, I tried ...
0
votes
1answer
192 views

Solve[polynomial, x, Reals] doesn't get all real roots or correct ones?

My main confusion is about the difference between the two code blocks at the end of this long spiel, but the spiel contains the code to create the polynomial if its coefficients are helpful for ...
1
vote
0answers
59 views

Finding undetermined coefficients with boundary conditions

I have 2 equations which are; To[x_] := c1 E^(-a1 x)/2 + c2 E^(a1 x)/2 + a2 Tu[x_] := c3 E^(-a3 x)/2 + c4 E^(a3 x)/2 Tu equals almost zero ...
2
votes
2answers
162 views

How to solve this numerically?

May I ask what is the best way to evaluate ...
1
vote
2answers
107 views

Given an equation with one parameter, how do I use NSolve to solve it for many values of the parameter?

I was wondering if there was a way to use the Mathematica NSolve command to solve an equation that has a parameter with various values. An example of which is: ...
2
votes
1answer
245 views
0
votes
1answer
35 views

Storing solution to x and y [duplicate]

If I do sol=Solve[{2x+2==y,3x+9==y},{x,y}] then Mathematica will tell me {{x -> -7, y -> -12}} But I would like to ...
0
votes
1answer
151 views

Non-linear equation system 3 equations and 3 variables [closed]

Can anyone please help me solve this system? 9.208x-3*y=0 -3x+3.208y+5*z=0 x^2+y^2+z^2=1 Thanks!
-2
votes
2answers
262 views

Solving a system of nonlinear equations? [closed]

I'm relatively new to using Mathematica so I'm not sure if this is really even possible, but I figured it may be worth a try. In my Physical Chemistry class today, we were learning about acid/base ...
3
votes
3answers
200 views

Simultaneous equations

I am trying to solve two simultaneous equations that are claimed to have 145 solutions but I believe they have 143, I want to check I am right before sending an email to my professor. Mathematica is ...
1
vote
2answers
93 views

Symbolic solution of system

everyone! I am sorry, but I am an abcolute novice of Mathematica (to be more precise this is my first day of using it) and even after surfing the web and all documents I am not able to solve the ...
0
votes
2answers
99 views

Solving a system of 4 logarithmic equations? [closed]

I would like to solve this system of 4 logarithmic equations in Mathematica. a*log(b+d)=20 a*log(b*30^c+d)=125 a*log(b*180^c+d)=710 a*log(b*360^c+d)=1350 I am looking for the values of a, b, c, ...
0
votes
2answers
93 views

Solving for any one variable in a formula given values for all the others [closed]

Consider the formula for the area of a rectangle. I can write the formula as area[length_, width_] := length*width and plug in numbers for the dimensions and get ...
0
votes
0answers
46 views

FindRoot to find numerical solution of a given index

I want to find solutions of a system of multivariate nonlinear equations of a specific index (i.e., the no. of positive eigenvalues of the Jacobian evaluated at the solution). I know the FindRoot ...
24
votes
3answers
7k views

Marking points of intersection between two curves

I'm trying to illustrate the solutions numerically and graphically for an equation such as Tan[x] == x. I think I did everything ok except I wanted to mark each ...
2
votes
0answers
38 views

Equation involving hypergeometric functions

I want to solve this equation but nor NSolve nor Solve are able to do this. ...
0
votes
0answers
43 views

How to obtain all minima? [duplicate]

If you Solve an equation, you obtain all solutions. But If you NMinimize a function, you only get one minimum. The question ...
1
vote
1answer
270 views

Solving Heat equation [closed]

I want to compute the exact solution of the heat equation but I got an error. u(x,t) (equation of transmition of heat) is the solution of this differential equation: $$du/dt - \alpha d^2u/dx^2 = 0$$ ...
3
votes
2answers
260 views

Intersection of Osculating Circle with a Parametric Curve

I have the following Parametric plot Generated from the following: ...
1
vote
2answers
123 views

Mathematica can't minimize a function

Mathematica seems not to be able to minimize this univariate function over integer arguments, $r>2, r \in \mathbb{Z}$. ...
2
votes
0answers
78 views

Deciding whether a semi-algebraic set is empty. Which command is best?

[Update] I was able to prove that the "larger" set $ 1\ge x \ge y,w \ge 0$ and $p(x,y,w)>0 $ is empty with another computer algebra system in my slow laptop in few minutes but in Mathematica even ...
0
votes
1answer
82 views

A question about using Reduce [closed]

Can someone help decipher what is the meaning of this computation that Mathematica has done? ...
1
vote
0answers
128 views

Calculating derivatives of roots of equation

I am interested in calculating how the roots of an equation change as one of the variables does, when the equation is evaluated numerically rather than symbolically. I have edited this code to be ...
0
votes
1answer
99 views

Numerical Methods - minimum of a function

Problem: The length of the longest ladder that can negotiate the corner depicted in Figure 2 can be determined by computing the value of theta that minimizes the following function: ...
0
votes
1answer
99 views

Trying to solve a transcendental equation involving bessel functions

I've never used Mathematica before and am trying to numerically solve equation (12) from this paper: http://arxiv.org/abs/hep-ph/9907218v2. Ideally I'd be able to find the smallest value of $x_{n\nu}$ ...
1
vote
0answers
77 views

What are the hidden specifications for FindRoot

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system" (or a nonlinear equation I ...
1
vote
1answer
112 views

Why does Mathematice dislike my boundary condition in NDSolve?

im trying to solve a PDE-System, with the "periodic boundary condition" c[t,0]==4*c[t,2pi] But mathenmatica says: NDSolve::bcedge: "Boundary condition ...
0
votes
1answer
73 views

Taking the time derivative of a function with more than one variable depending on t? [closed]

Yeah, I was wondering if it was possible ? I have a function which have different variables depending on time, like: $$\frac{d}{dt}mr^{2}\dot{\phi}$$ In this case both $r$, being a length, depends ...
0
votes
1answer
51 views

inverting this equation [closed]

I'm trying to inverse this equation Z = X + X^2 / 2 but couldn't wrap up my head around it. If anyone can provide a step by step solution to this it will be ...
1
vote
2answers
209 views

Symbolic solution of irrational equation

Is there any a nice looking solution to the following equation? eq[x_] := 2 x q1 - 2 q2/x^3 - (4 x^3 q3 - 4 q5/x^5)/(4 Sqrt[x^4 q3 + q4 + q5/x^4]) Better than ...
0
votes
1answer
329 views

How to find the inverse a symbolic matrix that Mathematica thinks might be singular

I have a square matrix depending on a parameter "a". When "a" has a numeric value (eg 2.1 * 10 ^ 8) through the inverse function Inverse[] I can invert the matrix. If I write the matrix as a function ...
1
vote
2answers
170 views

Why do Solve, NSolve, and FindRoot all fail on this simple, solvable actuarial equation?

If we express conditional mortality as a vector of annual probabilities of death, like so ...
0
votes
1answer
196 views

NDSolve example - analytical vs numerical solution. How to specify initial conditions?

So, I have the following equation: y[t]^-3 == w^2 y[t]/t^2 + y''[t] where w^2 = (t0 k0)^2. Analytic solution is easy to ...
0
votes
0answers
117 views

Mapping the imaginary axis of the complex (s) plane

In this problem is very difficult to analyze the roots s. Firstly I thought that the problem is in precision, but I am not sure. The criterion which I want to obtain is that one of these roots has a ...
1
vote
1answer
47 views

Invariant error plot for an arbitray system of ODE

i try to use InvariantErrorPlot command for a generic system of ODE but i find only example with pre-building equations from Mathematica Packages. This is one of ...
1
vote
1answer
141 views

How to solve that kind of partial fraction decomposition equations? [closed]

I need to find all variables $A, B, C, D$ for given equation with independent variable $s$. How can I solve that with Mathematica ? Example, not working: UPDATE: One Two Three Four ...
4
votes
3answers
183 views

How to find an approximate solution in a region when Solve or NSolve does not work?

Consider the relation x/Tan[Pi x] == y/Tan[Pi y] Solve or NSolve can't give a solution ...