7 votes
Accepted

How to solve differential equation with small values

Solve first for q[t],y[t] without using m[t] since m[t] is not coupled to the first two ...
Nasser's user avatar
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6 votes
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How can I find values of m so that the function $\frac{-m+x^2+x-4}{4 x-m}$ increasing in the interval $(1,2)$?

This can be done, making use of the definition of an increasing function and quantifiers or/and FunctionMonotonicity. ...
user64494's user avatar
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6 votes
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Bifurcation Analysis and Lyapunov Exponents Visualization

To solve this problem it could be better to define system of equations and Jacobian as expressions in a form of ...
Alex Trounev's user avatar
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6 votes
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How to solve this trigonometric equation to get -Sqrt[3]?

$Version (* "14.0.0 for Mac OS X ARM (64-bit) (December 13, 2023)" *) Clear["Global`*"] Use FunctionExpand...
Bob Hanlon's user avatar
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6 votes

Mathematica yields repeated solutions when only one exists

Have a look at Series[x Log[x] - 3/2 x - 1/(2 x) + 2, {x, 1, 4}] $$\frac{1}{3} (x-1)^3-\frac{5}{12} (x-1)^4+O\left((x-1)^5\right)$$ Its of course the trick to ...
Roland F's user avatar
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5 votes

Parabola from a focus and a directrix

The distance from the point {x,y} to the focus is equal to the distance from the point {x,y} to the line ...
cvgmt's user avatar
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5 votes

How to solve this trigonometric equation to get -Sqrt[3]?

RootApproximant ...
cvgmt's user avatar
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5 votes
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How to find number of integral solutions of the equation $\log _3(x+3 y)+x^2+3 y^2+4 x y-x-y=0$?

In view of the result of Factor[x^2 + 3*y^2 + 4*x*y - x - y] (x + y) (-1 + x + 3 y) the equality ...
user64494's user avatar
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5 votes

Calculating vertical displacement to intercept the perimeter of the circle after a horizontal shift

sol = First@ Solve[{x^2 + y^2 == 184^2, x == -17, y > 0}, {x, y}, Reals] {{x -> -17, y -> Sqrt[33567]}} ...
Syed's user avatar
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4 votes

How can I find values of m so that the function $\frac{-m+x^2+x-4}{4 x-m}$ increasing in the interval $(1,2)$?

A partial answer following your idea of studying $f^\prime(x)>0$. ...
mattiav27's user avatar
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4 votes

Mathematica 11.3.0, .nb file running for too long on Windows 10

...
Bob Hanlon's user avatar
  • 158k
4 votes

How to solve this trigonometric equation to get -Sqrt[3]?

...
MarcoB's user avatar
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4 votes

How to solve differential equation with small values

We can solve equations in two steps as Nasser mentioned, using NItegrate as follows ...
Alex Trounev's user avatar
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4 votes

Solve gives incomplete answer over complex numbers

...
Bob Hanlon's user avatar
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4 votes

ContourPlot does not draw intersection point and draws ragged plots

PlotPoints -> 50 will take care of the wiggles: ContourPlot[eqn1, {r, 1, 6}, {m, 0, 2}, PlotPoints -> 50] To get the contour line for the X point with eqn4, ...
Daniel Huber's user avatar
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3 votes
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Properly define function from outcome of NSolve and FindRoot

...
Bob Hanlon's user avatar
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3 votes

How to solve this trigonometric equation to get -Sqrt[3]?

-Csc[40 Degree] - Tan[10 Degree] /. Degree -> Pi/180 // RootReduce -Sqrt[3]
azerbajdzan's user avatar
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3 votes

How to find number of integral solutions of the equation $\log _3(x+3 y)+x^2+3 y^2+4 x y-x-y=0$?

May be you can try FindInstance ? ...
Nasser's user avatar
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3 votes

How do I erase sets of solutions from Solve based on criteria?

...
eldo's user avatar
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3 votes
Accepted

Calculating vertical displacement to intercept the perimeter of the circle after a horizontal shift

Assuming the circle with radius: r is at the origin. Then the top point has coordinates: r=184; top= {0,r} The point to the left with a displacement: dis of has ...
Daniel Huber's user avatar
  • 51.8k
2 votes
Accepted

Analytically solving this second order ODE

To eliminate the singlarity t==0(see my comment) try workaround ...
Ulrich Neumann's user avatar
2 votes

Parabola from a focus and a directrix

This is a partial "answer" to get you started. Play around with these ideas and if you are still stuck, then ask more specific questions. You can play with the underlying geometric semantics ...
lericr's user avatar
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2 votes

Solve third degree equation with functions as coefficients

If you'd accept a numeric solution, you could use ContourPlot: ...
march's user avatar
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2 votes
Accepted

Solve third degree equation with functions as coefficients

For the example you give there is a solution. However, for more general coefficients you may have to go numeric. sol = Solve[x^3 + Tan[t]*x + 1 == 0, x] There are ...
Hugh's user avatar
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2 votes
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Optimization for NSolve

...
ydd's user avatar
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2 votes
Accepted

How can we constrain this set of equations to obtain the desired form?

...
Bob Hanlon's user avatar
  • 158k
2 votes

How to solve a matrix differential equation $\frac{d X}{dt} = i(X Y- Y^\dagger X)$?

A brute force solution can be obtained by, first, defining ...
bbgodfrey's user avatar
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1 vote

How best to 2D plot nearly vertical function regions?

The objective seem purely visual as opposed to needing the ability to discern both an x and a y value from the figure. If so, why not just pick values for 2 line segments to fill in the gaps. ...
JimB's user avatar
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1 vote

Solve third degree equation with functions as coefficients

Here's a general solution: ...
Goofy's user avatar
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1 vote

Properly define function from outcome of NSolve and FindRoot

This is an abusing of NDSolveValue to solve non-differential equation by adding D[γ[u, v], v] to both sides of the equation. ...
azerbajdzan's user avatar
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