Questions tagged [equation-solving]

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

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2 votes
1 answer
173 views

Why does "Solve" not work for integral?

I have defined the following function: f1[c_] := -Integrate[E^(-t), {t, 0, y}] - Integrate[E^((-c)*t), {t, y, -Log[1/2]}] When I solve this for c=1, I get f1(1)...
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3 votes
2 answers
84 views

MeshFunctions in ParametricPlot with BSplineFunction for parameter extraction

I would like to use MeshFunctions in ParametricPlot in combination with BSplineFunction to ...
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-1 votes
0 answers
36 views

How can I loop a findRoot untill some condition has been met?

I need to do something quite simple. I have a findRoot, that in the end of the findRoot updates a number that changes the findRoots results. I need to repeat the findRoot until some condition is met. ...
-1 votes
0 answers
73 views

Solving to get the cosmological scale factor in units of length [closed]

The volume of the universe nowadays is a round $V= 10^{78} m^3$, does this mean the current value of the cosmological scale factor calculated by solving Friedmann equation is around $10^{26} m $ ? can ...
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0 votes
0 answers
53 views

How to solve a specific exponential equation where the power of the exponential function is a function of the variable to be solved

I want to solve "x" in the following exponential equations (1) A = x Exp[(m/x)+n x] (2) B = x Exp[(m/x)+x^n] where A, B, m and n are constants. I could easily solve A = x Exp[(m/x)] (the ...
0 votes
1 answer
96 views

Finding positive integer triples $(m,n,r)$ with $\frac{mr}{m+n}$ being an integer and $r-n > \frac{mr}{m+n}-1$ and $r\le \max{(m,n)}$ [closed]

I would like to use Mathematica to find all positive integer triples $(m,n,r)$ satisfying (1) $\frac{mr}{m+n}$ is an integer; (2) $r-n > \frac{mr}{m+n}-1$; (3) $r\le \max{(m,n)}$; (4) $1\le m < ...
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1 vote
1 answer
105 views

Trouble finding inverse of a function

I have the following Mathematica code: ...
  • 585
3 votes
1 answer
151 views

Issues with FindRoot. Getting error: FindRoot::eqlist: In the first argument {True,z1==0} only some of the components are equations

I am trying to solve a BVP for the system of equations. I need $r(0)$ and $\beta(0)$ to be fixed, and I need $r$ and $z$ to be fixed at the other end. I want $z(0)$ and the end value of $t$ to take ...
  • 55
4 votes
4 answers
192 views

Solving an equation using a list of values for a parameter

The MWE below Clear[p, x] p = -Sqrt[2]; {x1, x2} = x /. Solve[p x^2 + (1 + p^2) x + p == 0, x] solves the equation for the specific parameter $p=-\sqrt2$. How can ...
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0 votes
1 answer
62 views

Reducing an inequality with a complicated Log term?

I am trying to symbolically Reduce the following (admittedly complicated) inequality: ...
2 votes
1 answer
75 views

Reducing an inequality involving an exponential term?

I am trying to use Reduce to simplify the following inequality. ...
0 votes
0 answers
43 views

I am trying to solve this question but unable to solve the error message coming the length of the derivative operator Derivative[1] [closed]

...
-4 votes
1 answer
98 views

Finding solution to fourth order polynomial [closed]

I would have your opinion on this. So, we were assigned some questions to solve using the program Mathematica, but I am not sure how my teacher would like the solution to be presented. Could someone ...
1 vote
1 answer
55 views

How to Trace the message of Solve::ifun in DSolve?

I want to solve the D.E. about this: m l \[Theta]''[t] == -m g Sin@\[Theta]@t Then, I use Mathematica and type ...
1 vote
1 answer
73 views

How could I deal with and mark point of singularity or non-existance?

...
1 vote
1 answer
74 views

How to plot several lists for different values of independent variable in a same graph?

How could I plot parameters Br and Dr for several values of t0 starting from -3 to 0 with step size 1 for the following ode? I was able to plot t0=-3 and want to plot other lists of parameter set {Br,...
0 votes
1 answer
109 views

How to plot existance of solution vs non-existance for the following ode?

I want to plot solution region for the following ode for independent variable t=-7 to 0, and parameters,b=0.1 to 5,c=0.1 to 5, Br=0 to 4, Dr=20 to 40. The solution will not exist for every cases and ...
0 votes
2 answers
73 views

Is there an alternative way to obtain the given plot directly from the equation $f(a,b,x)=0$? [duplicate]

I have the equation $f(a,b,x)=0$ where the function $f(a,b,x)$ is as follows f[a_, b_, x_] := (x^2 + 2) (Sin[5 a] + Sin[3 b]) - 3 (x^2 + 1) Sin[x] I want to plot ...
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2 votes
1 answer
102 views

Unable to solve the given equation

I am trying to solve the given system in terms of $r$, for which I use the following code: ...
  • 585
0 votes
1 answer
69 views

How to plot the solutions of the equation $f_{a,b}(x)=0$ for $x$ as $a$ and $b$ range through the whole interval $(-2,2)$?

I have a three-variable function $f_{a,b}(x)$ for $x>0$, and $-2<a,b<2$, say f[x_,a_,b_]:=b^3 Sin[x] + Cos[a/b] Question I want to plot the roots of this ...
  • 1,089
0 votes
0 answers
50 views

Finding values of constants for which 1st and 2nd order derivatives of a function vanish

I'm trying to find critical values of some constants $v_c$ and $T_c$, for which holds the equality below: $$\bigg(\frac{\partial P}{\partial v}\bigg)\biggr\rvert_{v=v_c,\; T=T_c}=0,\quad \bigg(\frac{\...
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4 votes
1 answer
82 views

Order of solutions NSolve

I'm having a problem with Mathematica's NSolve function. I wrote the next example to illustrate the type of behavior that NSolve exhibits. ...
  • 455
1 vote
3 answers
109 views

Using FindRoot to find a Parameter

Let's say I have the typical harmonic oscillator ODE system = {x''[t] + x[t] == 0, x[0] == 1, x'[0] == Vi}; with undetermined initial velocity $...
3 votes
0 answers
69 views

Simplifying formula for a real-valued root of the quartic

I have a minimization problem which reduces a 4th degree polynomial with a real valued root. It's easy to get explicit formula for this root, but formula involves imaginary parts which always cancel ...
0 votes
2 answers
137 views

Roots of expressions involving the complementary error function

I have an expression as follows ...
  • 1,099
0 votes
0 answers
32 views

Limit of an infinitesimal imaginary part in Mathematica (revisited)

I have probably asked this question twice and my follow-up comment was deleted by the moderator, claiming that it is not an answer to the question. I will ask it once more, trying to be as clear as ...
0 votes
0 answers
113 views

Is there an analytic solution to this system of equations? If so, how can I obtain it? Mathematica is running forever

I am wondering whether there is an analytic (closed-form) solution for $a_S$ for the system of equations below. $\alpha_N$, $Y_S$, and $\epsilon$ are fixed (exogenous) parameters, and I am interested ...
1 vote
1 answer
148 views

Plot of massless particles on unstable null circular geodesic : Finding an alternative for Graphics`Mesh`FindIntersections and reducing code length

My friend and I were trying to reproduce Figure 4(left) from this paper(page 7). We succeeded in reproducing the result after writing a lengthy and complicated code. Here I dissect the code in steps: ...
  • 585
0 votes
0 answers
30 views

Converting Block to Manipulate and finding the intersection points [duplicate]

I have this Mathematica code which gives me the parametric plot of Free energy v/s Temperature at a constant value of Qt: ...
  • 585
1 vote
1 answer
74 views

How to use 'FindRoot' to get parameters by using solutions from ParametricNDSolve?

How could I get unknown parameters b,and c by using solutions from ParametricNDSolve? My solution working fine with single value for parameter Dr, but not working with list of values! Also, at the end ...
1 vote
2 answers
163 views

How to find the equation of a curve which is not symmetric [closed]

I need to find the equation of f1(x) by these three points (5,4) (2,5 , 0) (0, 1,5). I think it is not a standart symetric parabola.
0 votes
0 answers
56 views

Finding the coefficients that equate two sides of an equation

I have the following equation : $f(x)p(x)=g(x)p(\frac{x}{q}) + g(\frac{1}{xq})p(xq)$ q is a constant and $f(x)$ is a polynomial whose expression I have. Similarly $g(x)$ is also a known function. $p(x)...
0 votes
1 answer
74 views

Finding data of intersection points for a moving line and a curve from a parametric plot

I have the following Mathematica code to generate the plot of Lyapunov exponents v/s Temperature: ...
  • 585
0 votes
1 answer
70 views

Trouble with output of Reduce as a root object for a 3d Plot

I am trying to find the value of $r_0$ using $L^2=\frac{{r_0}^3 f'({r_0})}{2 f({r_0})-{r_0} f'({r_0})}$ and making a 3d plot with the help of the code given below: ...
  • 585
2 votes
1 answer
71 views

Struggling to get Solve to accept assumptions

I can't get Solve to solve the following two equations under the appropriate assumptions. When I enter ...
2 votes
2 answers
164 views

Solving nonlinear systems involving trigonometric functions [closed]

EDIT 1/2: "hardest?" geometry problem Triangle and sector areas are relatively easy to compute, first a numerical solution is attempted. For this interesting computation I intend giving ...
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3 votes
1 answer
142 views

Finding inverse of an algebraic function and using ListLinePlot

I am trying to find the Plot of Temperature v/s Free energy, for which I am using this code: ...
  • 585
1 vote
0 answers
55 views

How to determine why Mathematica killed an evaluation and cleared all variables? [closed]

I am curious if Mathematica stores a system log somewhere or if there is a way to set up my notebook such that it details why Mathematica silently kills an evaluation and clears all variables in the ...
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4 votes
3 answers
387 views

How can I reduce the time to solve this equation with Integral solutions?

I know that $\sqrt[3]{2744} = 2 + 7 + 4 + 4 - 3$, $\sqrt[3]{3375} = 3 + 3 + 7 + 5 - 3$, and $\sqrt[3]{4096} = 4 + 0 + 9 + 6 - 3$ by ...
1 vote
2 answers
56 views

Nsolve a parametric equation and using the result of NSolve in another equation

I have the following equation: (2 r)/(1 - 1/r + r^2 - r^(-1 + b)) - (r^2 (1/r^2 + 2 r - r^(-2 + b) (-1 + b)))/(1 - 1/r + r^2 - r^(-1 + b))^2 = 0 I need to find r ...
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10 votes
3 answers
283 views

Can NDSolve be initialized with a close solution?

I have a set of 4 first order ODE with 4 initial conditions to be met. It models a simple damped pendulum like the one described here. What changes is the damping term and I switched to first order ...
  • 879
0 votes
1 answer
56 views

Solve an equation in two variables containing symbolic constants

I've been struggling to solve equations in two variables containing constant symbolic parameters. Take for example the function in two variables defined by: ...
  • 153
1 vote
2 answers
165 views

Problem regarding "With" function

I am trying to calculate the effective potential using this code in Mathematica: ...
  • 585
1 vote
2 answers
67 views

Solve a parametric equation in 2 variables

I have a function in 2 variables $F(x,y)$, which also contains the constant parameters $\epsilon_{1}$, $\epsilon_{2}$,$\beta$. It is defined as: ...
  • 153
2 votes
2 answers
140 views

Solve equation in 2 variables

I have the following equation: $$f(x,y)+3=0$$ Where $$f(x,y):=2 \cos(\sqrt{3}y)+4\cos(\frac{3}{2}x)\cos(\frac{\sqrt{3}}{2}y)$$ My goal is to solve the first equation, i.e. find the points (x,y) such ...
  • 153
3 votes
4 answers
151 views

How to remove irrelevant terms (such as $\log$'s) in the solution of differential equation?

My input is the following: sol = DSolve[ (1 - 2/x) y''[x] + (2/x)*(1 - 1/x)*y'[x] - (2/x^2) y[x] == -1/ x^7, y[x], x ] Mathematica returns: ...
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0 votes
2 answers
49 views

Issue in combining FindRoot and NIntegrate

The following gives compile warnings and returns unevaluated, any idea why? ...
5 votes
2 answers
696 views

Why does mathematica repeat my differential equation again?Does it mean no solution?

I am trying to solve this \begin{equation} (1-\frac{2}{r})\partial_r^2 u+\frac{2}{r}(1-\frac{1}{r})\partial_r u+\frac{1}{r^2} \partial^2_x u+\frac{\cot x}{r^2} \partial_x u-\frac{\cos x}{r^2}(1+\frac{...
  • 191
6 votes
3 answers
523 views

How do I solve this matrix equation for infinitesimal rotations?

I have a matrix equation, taken from Wikipedia (Infinitesimale Drehungen), that looks not that complicated (note $a$ is a scalar, actually an angle as input paramter for the rotation matrix): $$ R(a)=\...
0 votes
1 answer
57 views

RecurrenceTable two difference equations

I have tried to use RecurrenceTable to Solve a system of two differential equations. I look for having a sequence of the two variables n (population growth factor) and w (wages). I have provided ...

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