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

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3
votes
1answer
234 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: ...
9
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
86 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
446 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
172 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 ...
0
votes
1answer
207 views

Searching for roots of complex function

I'm searching for roots of complex function $$ 2\imath q \ln(-2\imath k)+\imath\pi-2\imath \Im(\ln(\Gamma(1+2\imath q)))+\ln(\frac{\Gamma(1+\imath q-\imath q x/k)}{\Gamma(1-\imath q-\imath q ...
1
vote
0answers
50 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
142 views

How to solve this numerically?

May I ask what is the best way to evaluate ...
1
vote
2answers
79 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: ...
1
vote
1answer
172 views
0
votes
1answer
34 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
130 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
179 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
192 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
76 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
1answer
116 views

Solve non linear system of equations

I am trying to solve a system of two equations with two unknowns. In these equations I have, a part from constants: Unknown nr 1, $$D_{\perp}$$ Unknown nr 2, $$\omega_C$$ Known function of r: ...
0
votes
1answer
122 views

Solving a System of four equations (with logs)

I am trying to solve a system of four equations in four variables. I have read a number of threads on similar issues and tried to follow the suggestions. But I think it is a bit messy because of the ...
0
votes
2answers
87 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
85 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
1answer
95 views

Minimize: How to work with specific numeric types

This is a question about the use of symbols in Minimize and how to persuade Mathematica to treat them in a specific way (as integers or rationals) that I have not ...
-2
votes
0answers
52 views

periodicity of a solution of ndsolve pde

I am solving a pde with NDSolve and the solution is like U(x,t) which seems to be periodic and I am trying to find an algorithm to find the periodicity of such numerical solution. my code is like ...
0
votes
0answers
39 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 ...
23
votes
3answers
6k 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 ...
1
vote
0answers
30 views

Equation involving hypergeometric functions

I want to solve this equation but nor NSolve nor Solve are able to do this. ...
0
votes
0answers
42 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
119 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: $$du/dt - \alpha d^2u/dx^2 = 0$$ ...
2
votes
2answers
219 views

Intersection of Osculating Circle with a Parametric Curve

I have the following Parametric plot Generated from the following: ...
1
vote
2answers
91 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
69 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
77 views

A question about using Reduce [closed]

Can someone help decipher what is the meaning of this computation that Mathematica has done? ...
1
vote
1answer
114 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
68 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
63 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
54 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
79 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
64 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
50 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 ...
0
votes
2answers
193 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
175 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 ...
0
votes
2answers
135 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
140 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
106 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
42 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
144 views
1
vote
1answer
114 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 ...
3
votes
3answers
130 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 ...
0
votes
1answer
74 views

Numerical method for solving a polynomial equation

I am looking for a numerical solution of a equation which contains, in general, one polynomial equation with unknown variable x. I have tried Reduce, ...
0
votes
2answers
78 views

How to get a number from Solve [duplicate]

It's often useful to get just one number from Solve. I use the following construction for acquiring one solution from the expression returned by ...
0
votes
1answer
71 views

How to Solve/NSolve/Reduce this rationalized equation

In this problem I don't know why the system is not solvable. I have just one unknown K0. ...