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

learn more… | top users | synonyms (5)

2
votes
1answer
87 views

2D plot using output from the other function

I would like to get 2D plot using output from the other function. FindInstance[0.5*x^2 + Cos[y + P] == 1, {x, y}, Reals] By changing values of P manually it gives ...
2
votes
1answer
336 views

Potential flow over cylinder with FEM: Pressure field is flipped

Much in the fashion of a few problems already answered on Mathematica.SE (1, 2), I am trying to solve the Laplace equation in velocity potential $\phi$ to simulate irrotational, inviscid flow over a ...
2
votes
1answer
53 views

“Reduce” an expression in terms of a sub-expression

Newbie here. I've been trying to use Reduce to solve a rather long equation. The evaluation has been running for more than hour now, but still hasn't stopped. I've got an inkling that if I were to ...
2
votes
1answer
101 views

Implicit derivatives in one line. How do I do it?

I have this little script to derive implicitly $PrePrint = # /. {D[y_, x_, NonConstants -> {y_}] :> y'[x]} &; Example: ...
2
votes
2answers
170 views

Why does Mathematica not evaluate the difference recurrence using `RSolve` or `RecurrenceTable`?

Mathematica does not evaluate the following recurrence of two variables using RSolve and only echoes the input: ...
2
votes
1answer
178 views

Solving an integral equation numerically

my problem is: I get the result of definite integral and now I need to find the upper limit for the same integral but with opposite sign value so f2=-f1. ...
2
votes
2answers
158 views

Plotting the solution of a cubic equation against a coefficient in the equation

I have to plot the solution of the following equation against the coefficient $L$. Since it's a cubic equation, I'd like to filter out the real solution first and plot that then. The equation is $L r^...
2
votes
1answer
163 views

Mathematica - Count number of zeros of a function in an interval

Let's say I have a function, F[x_,d_] = Sqrt[(x^2 - 1)^2 + d^2], and I want to count how many roots (no root, or one root, or two roots etc.) it has in an ...
2
votes
2answers
2k views

Defining the domain of positive real numbers

I am trying to solve an equation by assuming that all the variables are real and strictly positive. I can use the keyword Reals for the argument ...
2
votes
1answer
123 views

Solving for flow speed?

I'd like to use Mathematica to verify the results of a Matlab code that iteratively solves for a flow velocity, u, given some fluid properties and a pressure drop. Ideally, I would like solve the ...
2
votes
3answers
162 views

Solving equation containing Erf expressions

Given the equation below, how do I find the value of b so that the function is equal to 21. I tried solve but I keep getting an error message. ...
2
votes
3answers
247 views

NSolve & PrecisionGoal

I am using NSolve to find numerical solutions of a particular equation. I do not need the solutions to as high of a precision as the other numbers in my notebook. To improve run time (I am iterating ...
2
votes
1answer
157 views

Computing Poincaré symbolic solution for an arbitrary integer order polynomial

In the 1880s, Poincaré created functions which give the solution to the nth order polynomial equation in finite form. These functions turned out to be "natural" generalizations of the elliptic ...
2
votes
1answer
143 views

Optimizing alphametrics code

First of all, thank you all in this great community. I have been reading a lot of threads about Mathematica optimization learning things like using Compile ...
2
votes
1answer
171 views

Seeking simple function in interval

I am a bit rusty, and struggling to solve this problem. Looking for a simple, well behaved parametric function f[t], from [0,1] to [0,1] such that: f[0] = f0; f[1] = f1; f'[1] = ff1; where -1<= ...
2
votes
3answers
100 views

Solve an equation for a product

I have an equation a = bcd/fg and I have another one that I can take bcd out of. Easy enough to do by hand, but Mathematica won'...
2
votes
1answer
117 views

Multiple dynamic equations for plotting?

Say I have a bunch of equations between variables e.g. h=bcd, i=hce, j=ihbd, ...
2
votes
2answers
226 views

Solving Differential Algebraic Equations as BVP

I am trying to solve a set of DAEs. \begin{equation} -4 \nu (\lambda(s))^{(-1 - 4 \nu)} \theta'(s) \lambda'(s) + (\lambda(s))^{(-4 \nu)} \theta''(s) = -\alpha_y \cos\theta(s) + \alpha_x \sin\theta(...
2
votes
2answers
227 views

Solving 4 variable system of equations

Trying to solve a systems of equations. Here's the code: ...
2
votes
2answers
337 views

How can I get Solve to combine Sin/Cos into Tan?

I want to solve an equation in x, containing Sin[x], Cos[x] and a positive real constant <...
2
votes
2answers
430 views

How to explain NDSolve that functions must be positive only?

I have a simple system of differential equations to solve but both functions should be positive: x[t] > 0 and y[t] > 0 for all t. I was not able to explain NDSolve this fact so it goes x[t] < 0 ...
2
votes
1answer
283 views

Find solutions of equation involving Bessel functions

I'm new in Mathematica and I'm trying to find the solutions of this equation involving Bessel functions $$\eta \frac{ J_{n+1}(\eta a)}{J_n(\eta a)}+\chi \frac{ I_{n+1}(\chi a)}{I_n(\chi a)}=0$$ ...
2
votes
3answers
895 views

Mathematica Solve function does not solve double exponential

I am trying to solve: Exp[-a Exp[-x/b] - c Exp[-x/d]] == Y to x, and using the command ...
2
votes
1answer
171 views

Simple differential equation to solve

Suppose we have this differential equation: $$ x^2 + y^2 + z^2 = \frac{\frac{\partial y}{\partial x}}{x+y+z}$$ I want to find $\frac{\partial y}{\partial x}$ at x=1,y=1,z=1. I tried this code but ...
2
votes
2answers
178 views

Graphical solution of a a two-variable system containing an equation and an inequality

I'm currently studying atmospheric-gravity waves and their dispersion relations. I want to have look at values of $(x,y)$ that solve the following system : \begin{equation}\label{}(1) \left\{ \...
2
votes
2answers
195 views

Quadratic Equations $\bmod p^k$

As part of a larger program, I need to solve $A x^2+B x+C \equiv 0 \pmod {p^k}$ for prime $p$. Right now I'm doing this by calling ...
2
votes
1answer
592 views

Resonance Curve using NDSolve

I am trying to make a resonance curve like this one below, using NDSolve. I tried to use code as below. Basically I try to hold solution for a w (driving frequency value) using NumericQ and then ...
2
votes
1answer
117 views

Plotting the solution of a 2nd order equation

I have got to solve a second order equation, where the coefficient depend on the parameter $k$: $$(A_k - \omega) (D_k- \omega) - B_kC_k = 0$$ so that also the solution $\omega=\omega(k)$ will depend ...
2
votes
1answer
495 views

Solving System of Inequalities Relatively

I have been trying to figure out how to solve a system of inequalities relatively. I don't care about values, I just want all possible ordering. An example system might be:$${b > r,\; p > r,\; c ...
2
votes
1answer
147 views

Compact form for domain ranges of many variables

When one sets up an equation to solve one often needs to specify conditions on the variables such as { x>0 && y>0 && z>0 } This is not ...
2
votes
2answers
807 views

How to make a Dynamic Calculator to solve a quadratic equation?

Taking my first steps in the world of Mathematica Programming. The aim of my program was to modify Wolfram's dynamic calculator (which performs an addition subtraction and a product - in response ...
2
votes
1answer
284 views

FindRoot equation-variable mismatch

I cannot figure out why FindRoot doesn't work and returns this error: The number of equations does not match the number of variables in ... My problem: drawing ...
2
votes
1answer
484 views

DSolve expression doesn't evaluate

Can Mathematica solve $\; d^2/dx^2{}+ (1/x) d/dx\;$ form of equations? For example, I am trying to solve the system of equations given below: ...
2
votes
2answers
2k views

How could I define a function as the solution of equations in Mathematica?

I have posed a specific question yesterday but it may be too trivial to answer. I think the question could be asked in a more general way so it is easier to answer. Then I could solve the original ...
2
votes
1answer
244 views

Finding the root of a nested function with small values

I have reduced an error in my program to this line of code: FindRoot[Nest[# (1 - #) k &, 1/2, 2^4] - 1/2, {k, 3.5}] It works for $2^1, 2^2, 2^3, 2^4,$ but ...
2
votes
2answers
2k views

Solving cubic equation for real roots

I'm looking to solve the following cubic equation for x: $\beta\, x^3 - \gamma \,x = c$. I have plugged in some sample values ($\beta = 2$, $\gamma = 5$ and $c = 2$). When I try to solve this ...
2
votes
2answers
571 views

How do I get the solutions of a cubic equation in trigonometric form?

I know $x^3-3 x+1=0$ has three roots that can be expressed in trigonometric form: $\{2\sin(10^\circ),\,-2\cos(20^\circ),\,2\cos(40^\circ)\}$. How can I get this result with Mathematica?
2
votes
1answer
144 views

What's the difference between the following two codes?

I have two codes to find the integer numbers $m$, $x$, $y$, $z$ in the system of equations. First code ...
2
votes
2answers
596 views
2
votes
1answer
200 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[] ...
2
votes
1answer
2k 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: ...
2
votes
1answer
52 views

Finding an Integer, Unimodular Matrix that connects two given matrices

I have two symmetric, integer matrices, $K$ and $K_2$ which have the same determinant and the same signature (number of positive - number of negative eigenvalues). I want to find an integer valued ...
2
votes
1answer
44 views

Help Compiling Vectors using Iterations

So I have a nice code that runs properly, which I include below but, in my naiveté, I'm having issues iterating my procedure. Simply put, I have a function of two real variables $f(x,y)$ and I want ...
2
votes
1answer
109 views

Complicated implicit plotting [closed]

I'm quite new to Mathematica and have already spent tons of time on problems of this type, browsing through tutorials and topics here. I'm now coming to conclusion that it cannot be done and am about ...
2
votes
1answer
127 views

Differential Equation with Numerically Integrated Boundary Conditions

I have a second order differential equation that I'd like to solve numerically, and then integrate its solution twice to get the parametric equations of a curve. The ODE is: $2 \kappa''(s)+\kappa^3(s)...
2
votes
1answer
49 views

Passing a list to a nested vector function

In order to apply a newton-rhapson algorithm to solve a set of nonlinear vector equations such as these, f[x_, y_] = {x^2 - 3*y + 6, (y + 1)^2 - x - 33} I need ...
2
votes
1answer
87 views

System of differential algebraic equations with one of the variables as an argument of the other varaibles

This is my first question here and I don't even know what to search for to find a solution. So I'd appreciate it even if someone can point me in the right direction. EDIT: My post had many problems, ...
2
votes
1answer
66 views
2
votes
1answer
80 views

Can not Solve FinancialDerivative for volatility

Although Solve can solve FinancialBond for an input parameter (e.g. par) given the price of a bond: ...
2
votes
1answer
136 views

How to handle a special Neumann-like boundary condition in NDSolve?

How to solve the following nonlinear ODE with two algebraic equations and one boundary condition? $$y''(x)=\dfrac{2\left((x+15)y'(x)-y(x)\right)\left(y'(x)^2+1\right)}{\left(y(x)^2+x(x+30)+236\right)...