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

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29 views

How can I select two lists from a list of lists so that I receive the system of equations has only rational solutions?

I want to make a sytem of equations has the form $$\begin{cases} a_1x^2+b_1y^2 + c_1xy+d_1x + e_1y+3=0,\\ a_2x^2+b_2y^2 + c_2xy+d_2x + e_2y+3=0. \end{cases}$$ so that the given system of equations has ...
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1answer
42 views

How do assign an interval of values to a variable in order to use them in a function?

From my code (below) I have K1 and K2 set to zero in order to test this numerical method. However, K1 is on an interval from 0 to 32, and K2 is on an interval from 0 to 8. I would like to know if ...
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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 ...
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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 ...
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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 ...
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1answer
224 views

Solving a System of four equations (with logs) [closed]

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 ...
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0answers
129 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 ...
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0answers
57 views

Gram Schmidt Process for functions [duplicate]

I want to implement the Gram Schimdt procedure to the space of functions in the following form \begin{align}‎ ‎R(y,x)=\left\{‎ ‎\begin{array}{ll}‎ f(x,y), ‎& y\leq x\\ \\‎ g(x,y), ‎& y>x‎ ...
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1answer
201 views

Unable to solve a set of equations with Solve

I'm trying to solve the following equation using Mathematica 9.0.1.0 : ...
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0answers
149 views

Solve[] unexpectedly giving empty solution sets for extremely large problems

I was calculating the set of lattice vectors in $\mathbb{Z}^4$ which have taxicab norm $r$. For example, executing ...
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0answers
88 views

No response from DSolve

Using optimal control theory, I am trying to find the optimal paths of d and k such that they will maximize profit as given by lc: ...
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223 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = ...
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199 views

Why DSolve and NDSolve give different answer

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? Which one is ...
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0answers
230 views

Solving asymptotic equations

Let's say I have several equations that have solutions given as a negative series $$y(t,x)=\sum_{n=-1}^\infty a_n(t) x^{-n}=a_{-1}x+a_0+a_1x^{-1}+\mathcal{O}(x^{-2})$$ My equations look like ...
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0answers
80 views

Simple Solve example fails: why? [duplicate]

Solve is an amazing tool, but sometimes it doesn't work in the way I expect it to. The particular instance that is confusing me right now is this: ...
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1answer
194 views

Gram Schmidt inner and outer products

I know the Gram-Schmidt orthogonalization generates an orthonormal basis from an arbitrary basis. I need help with: Write a program that inputs a list $\{b_1,\dotsc,b_n\}$ of linearly independent ...
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36 views

How can I access numerical values of variables calculated with Solve? [duplicate]

I am trying to calculate some thermodynamical cycles so I often use lists with equations. Here's a simple example: ...
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99 views
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167 views

Having Mathematica solve or help solve a set of 8 equations

There is a set of DDE's that arise in leukemia dynamics and I'd like to find the equilibrium points of the system by setting all of the derivatives equal to zero. The system can be described in ...
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0answers
65 views

Is it possible for Mathematica to give the step by step process of Reduce command? [duplicate]

Input: Reduce[3 x^2 - 2 a x + a^2 - 1 >= 0 && x > a, x] // TraditionalForm Output: ...
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0answers
126 views

Making simultaneous equation solving more efficient

I am trying to solve a system of several simultaneous equations that have been generated by a series of modules and functions, using this module: ...
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222 views

Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
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0answers
57 views

Finding Maximum Root [duplicate]

How can I find the greatest root for a polynomial if the polynomial degree is very large. One way is using NSolve. This command can find all roots in numeric. Then, ...
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88 views

Solving for vector elements in a function to which the vectors are not passed explicitly

I want to define a function which takes in two integers (indicating the lengths of 2 vectors), and solves a simple set of expressions at a set of points to find all the values in both the vectors. so ...
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0answers
190 views

Automatic inverse for Lambert’s Azimuthal Equal-Area Projection

I’m interested in finding closed-form inverses for map projection equations in general (of course, this is not always possible). I’m hoping Mathematica can help me with some of the trickier ones. As ...
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0answers
530 views

Calculating the mean curvature of a surface - suggestions

I am attempting to calculate the mean curvature [1, 2] of a surface defined by a function of x and y. My function is rather ...
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0answers
93 views

Symbolic FindInstance

I'm wondering if there is any way of doing something like the following: FindInstance[x < y, {x}, Reals] and getting, as a possible return value, ...
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3answers
161 views

Solving One Equation with Two Variables

I am trying to solve an equation with two variables. It is the last step in the process of using the method of undetermined coefficients to solve a nonhomogeneous differential equation. The equation ...
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2answers
140 views

Unexpected complex roots from solving a cubic

I am new to Mathematica and there is a behavior that I don't understand. When I insert the code: Solve[-(x - 2)^3 + 10 x - 10 == 0, x] I obtain: ...
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1answer
516 views

Solving linear equation

I want to solve following linear equations: \begin{align*} 3 x - y &= 0\\ y + 2 z &= -1\\ x + y + z &= 3 \end{align*} The output will be ...
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3answers
108 views

How to solve correctly inside a DO loop and then plot

Here is the corresponding code First the equations setup ...
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2answers
88 views

Gaps in plots of equation solution from parameter

I'm trying to plot solution of system of equations as a function of parameter ...
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2answers
192 views

Constraining two points, a specified distance apart, to a line

Suppose that I have two points in the xy plane: pt1 and pt2init. pt1 is fixed in space, ...
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1answer
93 views

How to calculate the unknown quantity in an infinite series?

I'd like to calculate x value in this equation. Basically, I tried to 2 types of method which are FindRoot and NSolve. But, I have failed the calculation caused by these errors up to now. If ...
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2answers
62 views

Solve prints message saying that it cannot solve my equation [closed]

I want to solve the fallowing equation: Solve[-(2/x^3) - 1/x^(5/2) - 1/x^2 + (4 Log[Sqrt[E] x])/x^3 == 0, x] Mathematica complaints: This system cannot be ...
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3answers
102 views

Partial products in prime steps [duplicate]

I am trying to find out partial products going up in prime steps for Euler's product formula $$\prod_{p} \frac{1}{1-p^{-s}}$$ Trying things like ...
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3answers
141 views

Solving algebraic equations

How may I make n and k in terms of x and y in this ...
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1answer
174 views

How to change machineprecision digits

I am trying to compute t0: ...
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3answers
189 views

Given a Boolean representation of a system, how can the Reliability Function be displayed as symbolic algebra?

Can Mathematica 9 convert a Boolean representation of an RBD to its symbolic algebraic form? If I have a simple series Reliability Block Diagram made up of 2 components, c1 and c2 bexpr1=And[c1,c2] ...
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1answer
220 views

Solve equation containing conditions (If expressions)

I want to solve the underneath equation. If I try Solve[AAA,dc], then I get no solution. Can anybody explain this? ...
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2answers
189 views

Derivative of the solutions by parameter

P0 = 0.1; K = 1000; Quiet[sol = Solve[{K*P*L == PL, P0 == P + PL, r*P0 == L + PL}, {P, L,PL}][[1]]]; complex = PL /. sol; Plot[complex, {r, 0.1, 2}] How can I ...
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1answer
187 views

x/.NSolve[f==g,x] does not work when f or g is the output of NDSolve!

I have been trying to put Points at the intersection of two curves, one of which is the ouput of a differential equation solved with NDSolve. The output being an Interpolation, NSolve cannot find the ...
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1answer
234 views

FindRoot on a 2D list of Equations

I have a $n \times k$ Matrix of data that I want to feed into an equation and solve for an unknown variable. I suppose I can always just convert the Matrix into a long Array but I'd like to learn how ...
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1answer
89 views

LinearSolve failing to find solution to system of linear equations of 64 variables

I've got a 64x64 Matrix L for which I want to find the solution to the matrix equation L . x == rho. L is defined as ...
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1answer
73 views

How can I speed up this multi-equation Solve problem?

I'm trying to solve a set of equations (chemical kinetics for a complex system, but don't worry about that). I ran it for 24 hours and I got no output. Here is the relatively simple code (I want to ...
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1answer
105 views

How to solve this nonlinear 2 by 2 equations?

I have a equation (x^2 + q1^2 - y^2)/2*(x + q1 - y) + (1 - 2*a)*q + 2*F = 2*(1 - a)*c[q] in q(variable) with parameters q1,a,F and function c(in variable q also, and I define it outside Solve so I can ...
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1answer
111 views

Finding the first five eigenvectors and values for a 500×500 matrix

I'm trying to find the first five eigenvalues and vectors of a matrix that has the following proporties: ...
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4answers
132 views

RSolve fails on a two-equation non-linear system

I have a system of just two recurrence equations, I need to solve them and so I use RSolve: ...
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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, ...
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2answers
86 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 ...