Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
3
votes
1answer
480 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
...
0
votes
1answer
104 views
0
votes
1answer
142 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
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
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 ...
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
$$\biggl(1+\dfrac{1}{x}\biggr)\cdot \biggl(1+\dfrac{1}{y}\biggr)\cdot ...
11
votes
2answers
367 views
NSolve gives additional solutions that don't satisfy the equations!
I am trying to solve the following polynomial equations in Mathematica:
...
1
vote
1answer
164 views
0
votes
0answers
120 views
Reducing a statement with Mathematica, step by step [duplicate]
Possible Duplicate:
Get a “step by step” evaluation in Mathematica
I have a list of inequalities combined with quantifiers. And Mathematica is able to reduce to simple statement with the ...
6
votes
3answers
233 views
Plotting $\omega(k_x, k_z)$ in $(\omega, k)$ plane with assumption of $k^2 = k_x^2 + k_z^2$
I'm currently studying atmospheric-gravity waves and their dispersion relations.
For analysis I need to plot the dispersion function:
\begin{equation}
\omega^4 - \omega^2\cdot C_s^2(k_x^2 + ...
4
votes
2answers
625 views
How do I work with Root objects?
I want to solve the trigonometric equation :
$$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$
I tried
Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x]
It returns the ...
2
votes
1answer
153 views
How to solve this exponential inequality?
I want to solve the exponential inequality $$8^x +18^x -2\cdot 27^x>0.$$ I tried
Solve[8^x + 18^x - 2*27^x > 0, x]
and
...
1
vote
0answers
77 views
Symbolic FindInstance
I'm wondering if there is any way of doing something like the following:
FindInstance[x < y, {x}, Reals] and getting, as a possible return value, ...
0
votes
0answers
273 views
Reduce/NSolve cannot solve a constraint problem?
I am trying to solve the following problem:
Minimize Integral[ (y''[x]+10)^2,x]
Where y''[x]+a*y'[x]+y[x] = 0, and the initial conditions for the DE are
...
2
votes
2answers
441 views
Why doesn't Mathematica solve $x=\cos\,x$ properly?
Why doesn't Mathematica solve x == Cos[x] properly?
Both Solve and NSolve fail with the ...
5
votes
4answers
749 views
How to solve this logarithmic equation?
The equation
$$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}$$
has two solutions for x, namely 1 and 2. I tried
...
1
vote
1answer
99 views
How to find the values of $m$ so $A \cap B = \emptyset$ and $A \cup B = (-3,+\infty)$?
I have two intervals $A = (-3, m^2- 2]$ and $B=[m, +\infty)$. How to find the values of $m$ so that $A \cap B = \emptyset$ and $A \cup B = (-3,+\infty)$?
I tried
...
3
votes
0answers
364 views
Solving a system of nonlinear equations self-consistently
I am trying to solve a set of three non-linear equations in Mathematica. I need help with them. The Mathematica code (in plain text format) is attached below. If you copy & paste the code below ...
1
vote
1answer
130 views
Using 'Reduce' to solve a set of inequalities, specified by a list
I have a two lists $LHS$ and $RHS$, both of size $n$. I want to solve a system of inequalities of the form:
$$LHS[1] \leq RHS[1]$$
$$LHS[2] \leq RHS[2]$$
$$LHS[3] \leq RHS[3]$$
$$\vdots$$
...
2
votes
1answer
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 ...
3
votes
1answer
396 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 ...
2
votes
1answer
298 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:
...
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 ...
1
vote
1answer
324 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 ...
-1
votes
1answer
296 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:
...
0
votes
1answer
145 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 ...
2
votes
1answer
141 views
Defining regions for `Exclusions`
I have the following function I want to plot in 3D (For simplicities sake we can say $a=5,b=-1,c=3$.)
...
8
votes
1answer
377 views
How do I find all the solutions of three simultaneous equations within a given box?
Sometimes, one needs to find all the solutions of three simultaneous nonlinear equations in three unknowns
$$\begin{align*}f(x,y,z)&=0\\g(x,y,z)&=0\\h(x,y,z)&=0\end{align*}$$
within a ...
3
votes
1answer
136 views
Tracking FindRoot errors in NestWhileList and Table
I'm solving many systems of two equations by varying the initial parameters. I'm running FindRoot in a NestWhileList where the ...
0
votes
0answers
81 views
Lost solution of the equation? [duplicate]
Possible Duplicate:
Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)
I solve the equation Power[x + 24, (3)^-1] + Sqrt[12 - x] == 6 ...
2
votes
1answer
227 views
How to solve simultaneous equations faster with Compile?
I have large 6x6 matrix Uwhich is a multiplication of 15 rotational matrix. All of the elements are Sin\[theta] and ...
1
vote
3answers
282 views
equation solving problems
I have some equation:
$$
veq=-2-lr-l^2r+2(r+ir^3\omega) v' + (-2+r)r^2v'^2 + (-2+r) r^2 v''==0
$$
or in Mathematica form:
...
5
votes
2answers
219 views
Reduce and Solve unable to solve equation
I have the following equation. Why aren't Solve and Reduce able to find the solution?
...
1
vote
2answers
206 views
Replacing variable in an equation with an Interpolating function polynomial and plotting residual
I was trying to plot the residual for the solution of my PDE. However, I was unsure about a couple of things.
I imported the data and created an Interpolation polynomial with ...
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 ...
5
votes
2answers
520 views
Solving a trig equation
I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ?
...
2
votes
1answer
327 views
Solving Simultaneous Equations
I am trying to solve two equations that take the form:
$W_0 \sqrt{1+\left(\dfrac{z}{\lambda\,\pi\, W_{0}^2}\right)}=W_1\;\,\quad \ldots(1)$
$W_0\sqrt{1+\left( \dfrac{z+0.1}{\lambda\, \pi\, ...
2
votes
1answer
211 views
How to solve a symbolic equation with symbols in powers
I am trying to solve
$\dfrac{\rho\ ((1-b)\ \lambda _f\ \lambda _s\ P _A)^{\rho }}{b-1}+\dfrac{\rho \left(\dfrac{b\ \text{ps}\ x}{1-\text{ps}}\right)^{\rho
}}{b}=0$
in terms of $b$,
I ...
0
votes
1answer
163 views
How to solve this equation? [closed]
The numbers real x and y, are solutions of the following equation system :
$$ \{x^3 + 3x^2y + 3xy^2 + y^3 2\sqrt2$$
$$ \{x^3 - 3x^2 + 3xy^2 -2y^3=0 $$ .
$$ x^2 + y^2$$
How to solve it ?
4
votes
1answer
440 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 - ...
16
votes
1answer
305 views
Why does repeating an equation help in FindRoot?
I'm trying to understand this behavior of FindRoot. Consider a sample function (the one I'm actually interested in is far more complicated, but has similar issues) ...
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):
...
5
votes
2answers
193 views
Solve for $a$ as a function of $\beta$?
I am trying to solve this equation:
$$\beta^{-a} \Gamma(a) \sin(a \pi) +
e^\beta \beta^{2 a - 1} \Gamma(1 - a) \sin(a \pi) = 0$$
I tried the following:
...
0
votes
1answer
164 views
Iterative way to find roots of confluent hypergeometric function
I am trying to find roots of confluent hypergeometric function and I wonder if I can choose the initial guess by the choice of $\beta$.
...
11
votes
4answers
354 views
How to make a Line[] with no end?
I'm trying to do this:
In this graph, the secant points are aproximated in order to become the tangent, it seems I need some kind of function which plots a line based on two points and it's points ...
