# Tag Info

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 ...
• 144k
Accepted

### 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. ...
• 26.4k
Accepted

### 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 ...
• 44.7k
Accepted

$Version (* "14.0.0 for Mac OS X ARM (64-bit) (December 13, 2023)" *) Clear["Global`*"] Use FunctionExpand... • 158k 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 ... • 3,622 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 ... • 73k 5 votes ### How to solve this trigonometric equation to get -Sqrt[3]? RootApproximant ... • 73k 5 votes Accepted ### 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 ... • 26.4k 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]}} ... • 54.2k 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$f^\prime(x)>0$. ... • 6,727 4 votes ### Mathematica 11.3.0, .nb file running for too long on Windows 10 ... • 158k 4 votes ### How to solve this trigonometric equation to get -Sqrt[3]? ... • 67.2k 4 votes ### How to solve differential equation with small values We can solve equations in two steps as Nasser mentioned, using NItegrate as follows ... • 44.7k 4 votes ### Solve gives incomplete answer over complex numbers ... • 158k 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, ... • 51.8k 3 votes Accepted ### Properly define function from outcome of NSolve and FindRoot ... • 158k 3 votes ### How to solve this trigonometric equation to get -Sqrt[3]? -Csc[40 Degree] - Tan[10 Degree] /. Degree -> Pi/180 // RootReduce -Sqrt[3] • 17.1k 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 ? ... • 144k 3 votes ### How do I erase sets of solutions from Solve based on criteria? ... • 70.4k 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 ... • 51.8k 2 votes Accepted ### Analytically solving this second order ODE To eliminate the singlarity t==0(see my comment) try workaround ... 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 ... • 28.2k 2 votes ### Solve third degree equation with functions as coefficients If you'd accept a numeric solution, you could use ContourPlot: ... • 23.5k 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 ... • 16.5k 2 votes Accepted ### Optimization for NSolve ... • 3,738 2 votes Accepted ### How can we constrain this set of equations to obtain the desired form? ... • 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 ...
• 61.5k
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. ...
• 41.7k
1 vote

### Solve third degree equation with functions as coefficients

Here's a general solution: ...
• 2,777
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. ...
• 17.1k

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