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### How do I get all the roots within a certain range for an equation? [duplicate]

I wish to find ALL the roots of the following equation $x \tan(ax) - c = 0$ within a range, where a and c are constants I control. I've been using ...
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### How to find x for certain y from InterpolatingFunction [duplicate]

As shown in the picture, I get the data after using NDSolve. Now I want to get the x for cetain y, how can I do this? The last three lines is the way I try to ...
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### How to find all the local minima/maxima in a range

I want to find : all local maxima in range all local minima in range From those points I can interpolate and combine functions upper and lower boundary. What I am really interested in, is the mean ...
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### How to find numerically all roots of a function in a given range?

It is common that I search numerically for all zeros (roots) of a function in a given range. I have written two simple minded functions that perform this task, and I know of similar functions on this ...
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### Solving this challenging ODE

Consider the ODE: $$w^{(4)}(x) + (L-x)w''(x) - w'(x) = 0$$ with some of the following boundary conditions: free: $w'' = 0$, $w'''=0$, clamped: $w = 0$, $w'=0$, pivot: $w = 0$, $w''=0$. Two such ...
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### NDEigenvalues vs. FindRoot for finding the eigenvalues of Airy equation?

Say I am trying to find the first 5 eigenvalues of the differential equation $f''(x)=\lambda x f(x)$, on the interval [-1,0], with boundary conditions $f(-1)=f(0)=0$. I will try to do this 3 ways, ...
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I'm solving the Schrödinger equation for a particle in an annular geometry with hard wall boundary conditions and I've reduced it to the following equation: $$J_m(k\,R_1)\,Y_m(k\,R_2) - J_m(k\,R_2)\,... 3answers 701 views ### How can I solve this equation: (47^{(u + 1)} + 3^{(u + 1)})/(u + 1) ==50^{1.5}/1.5? Solve[(47^(u + 1) + 3^(u + 1))/(u + 1) ==(50^1.5)/1.5,u] The code I tried is above, but it showed me a message problem "Solve was unable to solve the system ... 3answers 806 views ### Why does the following Solve take so long? Why does the following take Mathematica so long to reply to? Solve[BetaRegularized[0.5, k, n - k - 1] == 0.035, k] where n = 1000 By the way, In case there is ... 2answers 9k views ### Find all roots in range Is there any way to check for all roots in a range? Jens' findAllRoots function is pretty good, but runs at approx. 10% of roots missed when I ran a quick check on ... 2answers 604 views ### Techniques to find all local minima of black box function with n continuous derivatives? I have a blackbox function f on [a,b] that is known to be continuous, and has n continuous derivatives. The function uses polynomial interpolations (but isn't a polynomial interpolation itself), so no ... 2answers 2k views ### Find roots of a function involving Bessel functions I'm trying to find the roots of a function involving Bessel functions. Here is my code ... 2answers 286 views ### Eigen values of a third order linear homogenous ODE From a system of PDEs where i used the following ansatz:$$\theta_w(x,y) = e^{-\beta_h x} f(x) e^{-\beta_c y} g(y)$$. F(x) := \int f(x) \, \mathrm{d}x and G(y) := \int g(y) \, \mathrm{d}y So,$$\...
I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...