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

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1
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1answer
306 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
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1answer
206 views

How to solve this trigonometric system of equations numerically?

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

Solve not satisfying simple boundary conditions

I am trying to solve the following equations for the coefficients c1 and c2. ...
1
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1answer
86 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 ...
5
votes
1answer
318 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 ...
2
votes
0answers
347 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, ...
3
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1answer
268 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 ...
15
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1answer
338 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 ...
5
votes
2answers
271 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
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2answers
149 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 ...
8
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2answers
2k 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
594 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
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0answers
140 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
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1answer
141 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
2k 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 ...
1
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1answer
371 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 ...
6
votes
3answers
375 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 ...
2
votes
1answer
280 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
162 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}, ...
4
votes
2answers
243 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
397 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
537 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
191 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
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2answers
576 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
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0answers
549 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
189 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 ...
7
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0answers
178 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
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2answers
849 views

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

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

How to find 4 unknowns?

There are 4 unknowns constants: a,b,c,p. The variable is ...
0
votes
0answers
153 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 ...
2
votes
1answer
368 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
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0answers
94 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
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1answer
1k 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 ...
5
votes
4answers
1k 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
976 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 ...
1
vote
1answer
106 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
345 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
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0answers
903 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
326 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
432 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
1k 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
381 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 ...
10
votes
1answer
812 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 ...
-1
votes
1answer
717 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
242 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
337 views

Defining regions for `Exclusions`

I have the following function I want to plot in 3D (For simplicities sake we can say $a=5,b=-1,c=3$.) ...
4
votes
1answer
646 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 - ...