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

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5
votes
1answer
522 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
566 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
90 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
696 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
296 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
951 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
378 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
276 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
572 views
1
vote
1answer
194 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
557 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
956 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
442 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
159 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
214 views
0
votes
1answer
145 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
696 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
296 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
625 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
751 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" ...
15
votes
2answers
511 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
364 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
1k 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
605 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
208 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
1k 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
928 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
257 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
925 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
253 views

How to find 4 unknowns?

There are 4 unknowns constants: a,b,c,p. The variable is ...
0
votes
0answers
158 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
495 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 + ...
19
votes
2answers
4k 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 ...
3
votes
1answer
574 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
117 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
2k 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
108 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 ...
3
votes
0answers
1k views

Solving a system of nonlinear equations self-consistently

I am trying to solve a set of three non-linear equations in Mathematica. I need help with them. The Mathematica code (in plain text format) is attached below. If you copy & paste the code below ...
1
vote
1answer
707 views

Using 'Reduce' to solve a set of inequalities, specified by a list

I have a two lists $LHS$ and $RHS$, both of size $n$. I want to solve a system of inequalities of the form: $$LHS[1] \leq RHS[1]$$ $$LHS[2] \leq RHS[2]$$ $$LHS[3] \leq RHS[3]$$ $$\vdots$$ ...
2
votes
1answer
464 views

Vector Analysis: Why are the Grad, Laplacian and Div being evaluated to zero

For the non linear partial differential equation below, why are the Gradient, Laplacian and Divergence being evaluated to zero despite using the VectorAnalysis ...
4
votes
1answer
2k views

Finding the Minimum value of an interpolating function

I can't seem to use FindMinValue to find the min. value of a curve represented by an interpolating function. For instance the below code generates an interpolating ...
1
vote
1answer
496 views

2 non-linear equations with 2 unknowns which I cannot solve

I have the following equations and I would like to solve them in Mathematica anyway. Numerical results are very much welcomed. However, when I use the command ...
2
votes
1answer
1k views

'not a valid variable' error when trying to solve 13 equations with 13 variables

I want to solve 13 variables by 13 equations. And here is my program: ...
3
votes
1answer
853 views

Linear Solve with Modular Arithmetic

I am interested in using LinearSolve[m,b] which will find a solution to the equation $m.x=b$, where I am in mod 2 arithmetic. Is there any way to perform this ...
0
votes
1answer
1k views

Help to solve Simultaneous Equations

I think this should be easy to numerically solve in Mathematica, but for some reason I'm not finding the correct way to do it. I basically want to solve these simyltaneous equiations: ...