Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
5,783
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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)...
- 23
3
votes
2
answers
84
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MeshFunctions in ParametricPlot with BSplineFunction for parameter extraction
I would like to use MeshFunctions in ParametricPlot in combination with BSplineFunction to ...
- 33
-1
votes
0
answers
36
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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.
...
- 161
-1
votes
0
answers
73
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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 ...
- 297
0
votes
0
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53
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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 ...
- 85
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
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1
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105
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3
votes
1
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151
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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
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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 ...
- 1,273
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1
answer
62
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Reducing an inequality with a complicated Log term?
I am trying to symbolically Reduce the following (admittedly complicated) inequality:
...
2
votes
1
answer
75
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Reducing an inequality involving an exponential term?
I am trying to use Reduce to simplify the following inequality.
...
0
votes
0
answers
43
views
-4
votes
1
answer
98
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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 ...
- 23
1
vote
1
answer
55
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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
...
- 11
1
vote
1
answer
73
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1
vote
1
answer
74
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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,...
- 35
0
votes
1
answer
109
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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 ...
- 35
0
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2
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73
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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 ...
- 1,089
2
votes
1
answer
102
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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
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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
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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{\...
- 27
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
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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
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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 ...
- 6,441
0
votes
2
answers
137
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Roots of expressions involving the complementary error function
I have an expression as follows
...
- 1,099
0
votes
0
answers
32
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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
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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
1
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1
answer
148
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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
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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
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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 ...
- 35
1
vote
2
answers
163
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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
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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
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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
...
- 381
2
votes
2
answers
164
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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 ...
- 2,866
3
votes
1
answer
142
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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
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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 ...
- 11
4
votes
3
answers
387
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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
...
- 285
1
vote
2
answers
56
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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 ...
- 31
10
votes
3
answers
283
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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
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votes
1
answer
56
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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
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Problem regarding "With" function
I am trying to calculate the effective potential using this code in Mathematica:
...
- 585
1
vote
2
answers
67
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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
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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)$$
My goal is to solve the first equation, i.e. find the points (x,y) such ...
- 153
3
votes
4
answers
151
views
How to remove irrelevant terms (such as $\log$'s) in the solution of differential equation?
My input is the following:
sol = DSolve[ (1 - 2/x) y''[x] + (2/x)*(1 - 1/x)*y'[x] - (2/x^2) y[x] == -1/
x^7, y[x], x ]
Mathematica returns:
...
- 191
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votes
2
answers
49
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Issue in combining FindRoot and NIntegrate
The following gives compile warnings and returns unevaluated, any idea why?
...
- 6,441
5
votes
2
answers
696
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Why does mathematica repeat my differential equation again?Does it mean no solution?
I am trying to solve this
\begin{equation}
(1-\frac{2}{r})\partial_r^2 u+\frac{2}{r}(1-\frac{1}{r})\partial_r u+\frac{1}{r^2} \partial^2_x u+\frac{\cot x}{r^2} \partial_x u-\frac{\cos x}{r^2}(1+\frac{...
- 191
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votes
3
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523
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How do I solve this matrix equation for infinitesimal rotations?
I have a matrix equation, taken from Wikipedia (Infinitesimale Drehungen), that looks not that complicated (note $a$ is a scalar, actually an angle as input paramter for the rotation matrix):
$$
R(a)=\...
- 315
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votes
1
answer
57
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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 ...
