Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
3
votes
1answer
124 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 ...
3
votes
0answers
256 views
How can I solve this complicated custom function numerically?
I have a complicated function that calculates the total value of payments from an account into which deposits are made annually. I'd like to solve the function for a growth rate numerically, but ...
14
votes
1answer
241 views
Strange behaviour of Reduce for Mod[x,1]
For every integer $x$ the equation Mod[x, 1] == 0 holds. While
Simplify[Mod[x, 1] == 0, Element[x,Integers]]
gives ...
4
votes
2answers
199 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 ...
0
votes
2answers
83 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
197 views
4
votes
2answers
624 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
3answers
265 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 ...
8
votes
2answers
227 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
99 views
RSolve not returning known solution
I have the following recurrence relationship for which I know the solution is given by a binomial distribution:
...
0
votes
1answer
143 views
0
votes
1answer
115 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 ...
2
votes
1answer
829 views
Can Mathematica help to rearrange an equation?
I have an equation which I want to rearrange so one variable is on the left side by itself.
Normally, I would do this with basic algebra and identities.
However, is it possible to use Mathematica to ...
0
votes
1answer
492 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
0answers
306 views
Solving system of non-linear equations
I'm trying to plot the concentration of chemical reaction products (PL,PL,LPL) vs. molar ratio of initial components concentration (r). All concentrations are positive, rational and could not exceed ...
1
vote
1answer
127 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 ...
5
votes
3answers
297 views
Why don't I get numeric values from this Solve?
Solve[ a^2 + b^2 == c^2 && a < 100 && b < 100 && c < 100, {a, b, c}, Integers]
gives me this result
...
1
vote
0answers
132 views
Does Solve give every solution?
When I run the following:
Solve[{
ac == anc, ac == acn, ac == ancn,
acn == anc, acn == ancn,
anc == ancn,
q1 + q2 + q3 + q4 == 1
}, {q1, q2, q3, q4}
]
I ...
2
votes
1answer
121 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 ...
0
votes
1answer
77 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}, ...
8
votes
5answers
324 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" ...
0
votes
0answers
83 views
FindRoot is only passing two variables
When I run the code:
q0 = FindRoot[findarea[ch, rh, ah, lineh, intersecth, q][[1 ;; 2]] == ah[[1 ;; 2]]*r3^2,
{q, q0}][[1, 2]];
...
3
votes
1answer
475 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
208 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
...
2
votes
2answers
251 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
1answer
103 views
0
votes
1answer
141 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 ...
0
votes
2answers
148 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 ...
5
votes
2answers
272 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
253 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
120 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 ...
5
votes
0answers
119 views
What Method options does FindInstance accept?
While answering Trouble getting FindInstance to return multiple results for certain constraints it became clear that for this problem FindInstance would be better ...
11
votes
2answers
367 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
164 views
0
votes
0answers
120 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
233 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 + ...
2
votes
1answer
153 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
76 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
1answer
486 views
Solve in terms of specific variables
As part of my physics homework (which I do not need the answer for, as I did it by hand, and got the correct $$\frac{m_1 g-m_2 g \sin(\theta)}{-m_1-m_2}$$ as the answer) I would have liked to have ...
0
votes
0answers
271 views
Reduce/NSolve cannot solve a constraint problem?
I am trying to solve the following problem:
Minimize Integral[ (y''[x]+10)^2,x]
Where y''[x]+a*y'[x]+y[x] = 0, and the initial conditions for the DE are
...
5
votes
4answers
747 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
...
2
votes
2answers
440 views
Why doesn't Mathematica solve $x=\cos\,x$ properly?
Why doesn't Mathematica solve x == Cos[x] properly?
Both Solve and NSolve fail with the ...
1
vote
1answer
99 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
...
0
votes
1answer
199 views
(N)Solve does not solve equation
I am trying to calculate where a beam hits a mirror.
The mirror is described by this curve (two facing spherical mirrors):
...
3
votes
0answers
362 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 ...
2
votes
1answer
206 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 ...
1
vote
1answer
129 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:
$$LHS[1] \leq RHS[1]$$
$$LHS[2] \leq RHS[2]$$
$$LHS[3] \leq RHS[3]$$
$$\vdots$$
...
3
votes
1answer
394 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
237 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 ...
1
vote
0answers
89 views
Skip one step of the loop if there is NIntegrate::eincr: message
is there possibility to skip one step of the loop if in this step there appear error like NIntegrate::eincr:? For example: when I use "do" loop and when one of the step is evaluating I would like to ...
