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

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2
votes
0answers
329 views

FindRoot - Speed and errors

I am using FindRoot[] to solve a complicated equation. It seems I get the correct answer even though I get errors about an ...
13
votes
3answers
4k views

Find all roots of an interpolating function (solution to a differential equation)

I'm trying to find all the roots of the solution to a differential equation. Using NSolve or Reduce I don't get the roots, so I'm using an iterative method which I found in physicsforums.com. This ...
4
votes
3answers
894 views

Solving Integrals

Here's a problem that I don't understand. f[x_] := Exp[Cos[3*x]] g[x_] := (1/3)*x^3 - x^2 + 2 When I try to find the limit: ...
2
votes
0answers
101 views

Why cant Mathematica solve this equation? [duplicate]

Possible Duplicate: Can Reduce *really* not solve for x here? Why cant Mathematica solve this equation? ...
1
vote
1answer
572 views

How to extract Solve results as variables [duplicate]

Possible Duplicate: Assign the results from a Solve to variable(s) In the following example: ...
4
votes
1answer
231 views

How to solve this trigonometric system of equations numerically?

How can the following trigonometric system of equations be solved numerically? ...
0
votes
1answer
250 views

Solve not satisfying simple boundary conditions

I am trying to solve the following equations for the coefficients c1 and c2. ...
2
votes
0answers
458 views

Numerically/Analytically Solving a System of Equations

I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
5
votes
1answer
456 views

Using external variable as a variable inside WhenEvent & NDSolve

I'm trying to use the new WhenEvent functionality of NDSolve in Mathematica 9, in order to perform an action when a variable in the system reaches a certain value. I would like this variable to come ...
4
votes
1answer
437 views

Find asymptotics of a function

Can Mathematica find the asymptotics of a function in the following sense? I have Log[1/n^2]/Log[4^(-Sqrt[Log[n]]) + (2^(-Sqrt[Log[n]]) - 1)^2] and I would like ...
1
vote
1answer
88 views

How to get a solution involving logs in the right form?

How do I get Solve[(1/9)^(r/2) == 1/n , r] to give me Log[n]/Log[3] and not ...
9
votes
2answers
626 views

Solving/Reducing equations in $\mathbb{Z}/p\mathbb{Z}$

I was trying to find all the numbers $n$ for which $2^n=n\mod 10^k$ using Mathematica. My first try: Reduce[2^n == n, n, Modulus -> 100] However, I receive ...
5
votes
2answers
287 views

How to solve this combination equation?

I want to solve the equation $$ 2n\cdot\binom{n}{0} + 5(n-1)\binom{n}{1}+13(n-2)\binom{n}{2}+\cdots + \left(2^{n-1} + 3^{n-1}\right)\binom{n}{n-1} = 1685. $$ or using alternative notion for binomial ...
1
vote
1answer
866 views

How can I understand the result Mathematica returns from DSolve?

I have solved an ODE using DSolve, but I have a problem with understanding the solution. In general the solution is in the form: ...
4
votes
1answer
363 views

Eliminating functions from system of PDE in Mathematica

Mathematica users, Let's see an example of three PDEs: How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
0
votes
2answers
245 views

How to use Solve rules as a function body?

Solve gives me an expression which I want to use as the body of a function. Rather than run Solve every time inside my function ...
2
votes
2answers
533 views
1
vote
1answer
186 views

Remove failed Solve[] attempts

I can't figure how to replace a failed evaluation with a null value. I am very new to Mathematica. I have an equation that are being processed using the Solve[] ...
7
votes
3answers
538 views

NDSolve and {C, K, Slot} and other built-ins as a variable name

The following problem is an exploration of what causes the error "Input is not an ordinary differential equation" in Mathematica as it seems to have changed from version 8 to version 9. Specifically ...
3
votes
3answers
824 views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
13
votes
2answers
427 views

Is there a way to use functions like Prime[n] within Solve[]?

I'm trying to see if a number can be written as the sum of two prime numbers. Ideally, I would like to use Solve[ Prime[n] + Prime[m] == 100, {n, m}] But that ...
3
votes
0answers
153 views

RSolve not returning known solution

I have the following recurrence relationship for which I know the solution is given by a binomial distribution: ...
1
vote
1answer
207 views
0
votes
1answer
143 views

Industrial Level Applications. Recipe for mixed notation of equations set

I am working with large (linear) equations set within Mathematica in numerical notation. For example, set from 4056 eq. is solved for a second, no more. There is no doubt, result is great. But even ...
1
vote
1answer
618 views

Comparing two symbolic expressions

Does Mathematica provide any way to compare two symbolic expressions and find which is the greatest? For example, I want to find which is the greatest of ...
1
vote
3answers
2k views

Tricks for solving (lots of) coupled nonlinear equations numerically?

I have a system of 6 non-linear (quadratic) coupled equations with 6 complex unknowns \begin{align*} |x_1|^2 + |x_2|^2 + |x_3|^2 &= a\\ x_1 x_4^* + x_3 x_5^* &= b + c i\\ x_1 ...
0
votes
1answer
250 views

Assign the result of Solve in a list [duplicate]

Possible Duplicate: Assign the results from a Solve to variable(s) I want to assign the results of a Solve command in a list. For example Solve[-((287 s^3)/50) == 0, s] returns {{s -> 0}, ...
2
votes
1answer
481 views

How to modify a matrix to satisfy a special condition?

I have matrix like this: How do I modify this matrix to make it satisfy the following condition: For each element {i, j} in the matrix the sum of the elements of row i must be equal to the sum ...
9
votes
5answers
692 views

Create filling between two trig functions

Working with trig functions, period, amplitude, etc. I found a worksheet at a calculus website, with some nice questions related to interpreting trig functions, at least, they provide some "fun" ...
14
votes
2answers
462 views

Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, ...
8
votes
2answers
2k views

NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
4
votes
2answers
322 views

Both Sin[x]==0 && Cos[x]==0 as a solution

If I do FullSimplify[Reduce[Sin[p1] == 0 && Cos[p1] == 0, Reals]] I get Cos[p1] == 0 && Sin[p1] == 0 ...
0
votes
1answer
875 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 ...
2
votes
2answers
534 views

FindRoot errors

I'm trying to solve a system of two equations in two variables for some range of parameter values. I use ContourPlot to see where I should look for a solutions and ...
0
votes
2answers
203 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 ...
6
votes
2answers
897 views

Solve an equation in $\mathbb{R}^+$

How can I solve this equation (both numerically and literally) only in the positive reals $\mathbb{R}^+$? Solve[x == (v0 - (A CD t v0^2 ρ)/(4m)) Cos[θ] t, t] And ...
1
vote
0answers
821 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 ...
0
votes
1answer
237 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 ...
3
votes
1answer
809 views

How to solve this equation with positive integers as a solutions?

This is a problem of United Kingdom Mathematical Olympiad. Find all triples $(x,y,z)$ of positive integers such that $$\biggl(1+\dfrac{1}{x}\biggr)\cdot \biggl(1+\dfrac{1}{y}\biggr)\cdot ...
14
votes
3answers
1k views

NSolve gives additional solutions that don't satisfy the equations!

I am trying to solve the following polynomial equations in Mathematica: ...
1
vote
1answer
243 views

How to find 4 unknowns?

There are 4 unknowns constants: a,b,c,p. The variable is ...
0
votes
0answers
157 views

Reducing a statement with Mathematica, step by step [duplicate]

Possible Duplicate: Get a “step by step” evaluation in Mathematica I have a list of inequalities combined with quantifiers. And Mathematica is able to reduce to simple statement with the ...
6
votes
3answers
469 views

Plotting $\omega(k_x, k_z)$ in $(\omega, k)$ plane with assumption of $k^2 = k_x^2 + k_z^2$

I'm currently studying atmospheric-gravity waves and their dispersion relations. For analysis I need to plot the dispersion function: \begin{equation} \omega^4 - \omega^2\cdot C_s^2(k_x^2 + ...
18
votes
2answers
3k views

How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
2
votes
1answer
510 views

How to solve this exponential inequality?

I want to solve the exponential inequality $$8^x +18^x -2\cdot 27^x>0.$$ I tried Solve[8^x + 18^x - 2*27^x > 0, x] and ...
1
vote
0answers
113 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, ...
2
votes
2answers
1k views

Why doesn't Mathematica solve $x=\cos\,x$ properly? [duplicate]

Why doesn't Mathematica solve x == Cos[x] properly? Both Solve and NSolve fail with the ...
5
votes
4answers
2k views

How to solve this logarithmic equation?

The equation $$x^2\cdot\log_2\dfrac{3+x}{10}-x^2\cdot\log_{\frac{1}{2}}(2 + 3x)=x^2 - 4+2\cdot\log_{\sqrt{2}}\dfrac{3x^2+11x+6}{10}$$ has two solutions for x, namely 1 and 2. I tried ...
1
vote
1answer
107 views

How to find the values of $m$ so $A \cap B = \emptyset$ and $A \cup B = (-3,+\infty)$?

I have two intervals $A = (-3, m^2- 2]$ and $B=[m, +\infty)$. How to find the values of $m$ so that $A \cap B = \emptyset$ and $A \cup B = (-3,+\infty)$? I tried ...