Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
4
votes
2answers
212 views
All possible solutions to the Matrix Equation (free variables appearing)
I am attempting to solve a system of linear equations using LinearSolve[] . In my case, the number of unknowns are more than constraints. I learnt that LinearSolve ...
4
votes
2answers
478 views
4
votes
4answers
366 views
recursively solve equation and saving the values
I am new to Mathematica. I am trying to recursively solve an equation and saving the values into a Table. Since I need the real solutions only I use ...
4
votes
2answers
143 views
Finding all/most roots of a discontinuous function more consistently?
I have the equation:
f[x_]:=α Tan[α*a] - Sqrt[c - α^2]
and ideally I want to find all of its positive zeros, given a and c, with variable alpha. The problem is ...
4
votes
1answer
444 views
Reduce an equation by putting a new variable
I have the following equation given:
$$ (26-x)\cdot\sqrt{5x-1} -(13x+14)\cdot\sqrt{5-2x} + 12\sqrt{(5x-1)\cdot(5-2x) }= 18x+32. $$
In order to solve it, I want to substitute $t = \sqrt{5x - ...
4
votes
2answers
134 views
Using RSolve correctly
I am having problems persuading Mathematica to solve even the simplest recurrence relations. As an example, how would you do the following?
...
4
votes
3answers
227 views
Replace function and its derivatives found with Solve
If I have an equation
eq = f[x] + g[x] == 0
and I solve for f[x]
sol = Solve[eq,f[x]]
...
4
votes
2answers
124 views
find where 3 inequalities are simultaneously greater than zero
I have 3 functions, f11[l], f12[l] and f13[l], and I would like to know for which values of l these 3 functions are greater than zero. How do I do it analytically or numerically or graphically in ...
4
votes
2answers
133 views
How can I eliminate equivalent equations from a list?
I want to find the numbers $a$, $b$, $c$, $d$ of the plane $ax + by +cz +d = 0$ which make the distance from the point $M(1,2,3)$ to the plane equal to 2. I tried
...
4
votes
1answer
366 views
How Can I use Solve/Reduce Output
Suppose I want x and y to be rationals
Solve[ x^2 + y^2 == 1, {x, y}, Rationals]
I am ...
4
votes
1answer
248 views
How do I use RSolve to solve a system of recurrence relations?
I am trying to solve a system of recurrence relations as follows.
...
4
votes
1answer
62 views
Trouble using FindInstance with MatrixRank
I'm really confused about what's going wrong with my call to FindInstance:
...
4
votes
3answers
788 views
Backsubstituting solution into FindRoot
I am trying to solve a system of equations which is dependent to an parameter alpha. So I iterate over alpha via a ...
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
...
4
votes
1answer
141 views
Can mathematica resolve this equation?
Obviously，the equation $x^2-3 y^2=2 z^2$ doesn't have positive integer solutions.
I tried
...
4
votes
1answer
572 views
Efficient implementation of cubic equation of state
...In this case the Peng Robinson Equation of State. Equations of state are empirical equations with parameters derived from experimental data. They are used to predict pure component and mixture ...
4
votes
1answer
272 views
Solving recurrence relation using Mathematica defined in a piecewise way
I have a recurrence relation defined as following:
RSolve[
{
p[0] == p0,
p[1] == λ p[0]/μ,
p[i + 1] == λ p[i]/(2 μ)
},
p[i], i
]
Note that the relation ...
4
votes
2answers
82 views
Extracting Reduce results
I'm solving a Diophantine equation inside of a function using Reduce but I'm having trouble extracting the necessary parts of the answer.
For example, if my input ...
4
votes
1answer
184 views
NDSolve does not respond
For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
4
votes
0answers
165 views
Incompleteness of FindInstance
I've been playing around with Resolve and FindInstance. I know that Resolve should always ...
3
votes
3answers
283 views
How to obtain a fixed number of solutions to $x+y=1$?
How to obtain a fixed number of solutions to $x+y=1$?
For example, I want 4 solutions:
$(1,0),(2,-1),(3,-2),(-2,3)$
I want to do this also on bigger equations such as $x+y+...=1$ and then I want to ...
3
votes
3answers
205 views
Efficient code for solve this equation
We have know $a*b*c=-1$, $\frac{a^2}{c}+\frac{b}{c^2}=1$, $a^2 b+a c^2+b^2 c=t$,
What's the value of $a^5 c+a b^5+b c^5$?
I tried
...
3
votes
3answers
267 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 ...
3
votes
2answers
1k views
How to convert a system of parametric equations to a normal equation?
For example, I have a system of parametric equations (R is a constant number) :
...
3
votes
2answers
206 views
Mathematica does not understand (R^3)^(1/3) is the same as R [closed]
In the output from a calculation in mathematica stands a/((R^3*c)^(1/3)), with c and a ...
3
votes
3answers
1k views
How to get rid of warnings when using Solve on an equation with inexact coefficients?
When I solve this equation in Mathematica 8, I can get the right answer, but with some uncomfortable warnings.
Equation:
...
3
votes
4answers
888 views
Solving complex equations
I feel like I am missing a basic, but key point when using Mathematica's Solve or Reduce.
...
3
votes
2answers
135 views
3
votes
1answer
148 views
What properties make this equation difficult to symbolically solve?
I tried to solve the following equation with Mathematica's solve:
Solve[K*(2*Tan[L/2*Sqrt[P/(EI)]]-L*Sqrt[P/(EI)])+4*P*Sqrt[P/(EI)] == 0, P]
It gave the ...
3
votes
1answer
459 views
Solving an Integral equation
I would like to solve the equation
$$\frac{2}{p}\int_0^1((1-u)^{1-p}+u^{1-p})^{\frac{1}{p}}\text{d}u=42$$ for p numerically.
I tried
...
3
votes
1answer
99 views
Solving an inequality that contains Log expressions
How can I solve the following inequality? I tried the command Reduce, but the computer is still computing it (c is an real number).
...
3
votes
2answers
353 views
Solving a linear equation in Mathematica
This should be easy but I can't seem to find the right way to do it.
I have an equation of the form $a x + b x + c y + a z + d z = 0$, and I'd like to solve for relations between the parameters ...
3
votes
1answer
174 views
Create Euler equation
I've tried to make some research, but without any luck.
How do I setup the Euler equation for this in Mathematica?:
$ \text{Min} \int_0^1\left(2x^2+ \left(4t-5 e^{r \, t} \right) x \, \dot{x} + ...
3
votes
2answers
178 views
How can I solve an equation with symbolic coefficients?
I want to try to solve the following
a x^(17/6) - b x^2 - 1 == 0
where a and b are ...
3
votes
1answer
491 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 ...
3
votes
2answers
683 views
Select Solution with real (positive, etc) coefficients - ignoring variables
I often need to solve equations for numerical coefficients while preserving numerous variables (e.g. to preserve scaling relations). Thus I end up with a set of solutions like
$$
...
3
votes
3answers
95 views
Inverting a Spline-Function (Bezier or BSpline)
I would like to use a Spline-Function to describe a transformation from one range of reals to another, that is I would like to have a function which maps a value $y$ on $x$ and for simplicity let us ...
3
votes
3answers
307 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:
...
3
votes
1answer
117 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 ...
3
votes
2answers
308 views
Is there a way to solve the Apollonius Circle problem in Mathematica?
Assuming x, a, and b are complex numbers, is there a way to reduce the equation Abs[x - a] == k Abs[x - b] to something like ...
3
votes
2answers
162 views
Why didn't Reduce give me the right result?
My code:
Clear[r1, r2];
par[r1_, r2_] := r1 r2 / (r1 + r2);
Reduce[{5 par[r2, 32000]/(r1 + par[r2, 32000]) == 1.8 && par[r1, r2] == 5000}, {r1, r2}]
...
3
votes
3answers
253 views
Animate a position change along the curve for every iteration
I've only had few previous experiences on Mathematica before. So basically an entry-level question that harasses a rookie like me.
I made the following attempt using bisection method to calculate ...
3
votes
1answer
88 views
How can I get a single solution to a set of inequality constraints?
I have a set of constraints to which I require integer solutions. However, instead of needing all possible integer solutions (as obtained by using ...
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
1answer
279 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 ...
3
votes
1answer
222 views
Selecting polynomial roots and plotting against parameters
An implicit function $f(x,k)=0$ is quadratic in $x$ and contains one
parameter $k$ which I must vary.
Using Solve, I get two real solutions for each specific $k$: ...
3
votes
1answer
798 views
Why can't Mathematica “Solve” my equation?
I am trying to get Mathematica to solve the following equality in terms of $w_i$
$\displaystyle \frac{\sum_{i = 1}^{n} x_i }{\sum_{i = 1}^{n} y_i} = \frac{\sum_{i = 1}^{n} ( (\frac{x_i}{y_i}) w_i ) ...
3
votes
1answer
78 views
Cannot solve system of linear equation sums?
I cannot get mathematica to solve:
The problematic code:
...
3
votes
2answers
154 views
Eliminate several variables between five Conic_section equations
I want to eliminate x1, x2, y1, y2 between these 5 equations.
I tried
...
3
votes
1answer
402 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 ...
