Question

Prove $x^2 = \sin(x) $ has exactly two solutions on $[0, \pi/2]$

score 3.6k · Answer 1 · 2017-04-07 08:20:40

3.6k

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Prove $x^2 = \sin(x) $ has exactly two solutions on $[0, \pi/2]$

Published on 07 Apr 2017 - 8:20

score 100 · Answer 2 · 2023-02-09 22:52:21

100

Views

How can you determine if a transcendental equation has elementary solutions or not?

Published on 09 Feb 2023 - 22:52

score 429 · Answer 3 · 2023-02-28 23:18:39

429

Views

Closed-form solution to the transcendental equation

Published on 28 Feb 2023 - 23:18

score 92 · Answer 4 · 2023-03-20 03:10:43

92

Views

Find the condition such that $A \cos{x} = x$ has exactly two solutions.

Published on 20 Mar 2023 - 3:10

score 85 · Answer 5 · 2026-02-23 06:38:08

85

Views

How to solve $\,A\sin(\theta_2-\theta_1) - B\sin(\theta_1) = 0$

Published on 23 Feb 2026 - 6:38

score 69 · Answer 6 · 2023-03-25 12:11:27

69

Views

How to solve $x^x = n$ algebraically?

Published on 25 Mar 2023 - 12:11

score 635 · Answer 7 · 2023-04-02 08:12:37

635

Views

Closed form for zeros of a function

Published on 02 Apr 2023 - 8:12

score 175 · Answer 8 · 2026-02-24 05:20:00

175

Views

Convert $\frac1b\sum_{n=1}^\infty\frac{(b e^a)^n}{n!}B_{n-1}(an)$ to integral using $B_n(x)=\frac{n!}{2\pi i}\oint\frac{e^{x(e^t-1)}}{t^{n+1}}dt$

Published on 24 Feb 2026 - 5:20

score 34 · Answer 9 · 2026-02-24 05:21:10

34

Views

Evaluate $\frac{d^{n-1}}{dw^{n-1}}\csc^{-1}(w)^n$ or $\frac{d^{n-1}}{dw^{n-1}}\left(\frac{\sqrt{w^2-1}+i}w-1\right)^m$

Published on 24 Feb 2026 - 5:21

score 73 · Answer 10 · 2023-05-06 17:56:36

73

Views

Study number of complex zeros of a function contained in a strip

Published on 06 May 2023 - 17:56

score 109 · Answer 11 · 2023-05-24 17:52:46

109

Views

Can anyone enlighten me on $e^{-x} = \alpha x$

Published on 24 May 2023 - 17:52

score 261 · Answer 12 · 2023-05-30 00:10:16

261

Views

Find $\int_0^\frac\pi2e^{i(ut+v\cos(t))}dt$ or $\int_0^\frac\pi2\sin(w+ut+v\cos(t))dt$ to invert $\frac{\sin(x)}x$

Published on 30 May 2023 - 0:10

score 170 · Answer 13 · 2023-06-16 19:41:38

170

Views

Exact solution to the the equation $(2 \pi - \theta)\cos \theta + \sin \theta = 0$

Published on 16 Jun 2023 - 19:41

score 433 · Answer 14 · 2023-06-27 18:06:13

433

Views

How can we find Lambert W solution to $\dfrac {x\ln x}{\ln x+1}=\dfrac{e}{2}$?

Published on 27 Jun 2023 - 18:06

score 142 · Answer 15 · 2023-09-29 07:00:42

142

Views

Solving $\frac{8^x-2^x}{6^x-3^x}=2$

Published on 29 Sep 2023 - 7:00

List Question

Prove $x^2 = \sin(x) $ has exactly two solutions on $[0, \pi/2]$

How can you determine if a transcendental equation has elementary solutions or not?

Closed-form solution to the transcendental equation

Find the condition such that $A \cos{x} = x$ has exactly two solutions.

How to solve $\,A\sin(\theta_2-\theta_1) - B\sin(\theta_1) = 0$

How to solve $x^x = n$ algebraically?

Closed form for zeros of a function

Convert $\frac1b\sum_{n=1}^\infty\frac{(b e^a)^n}{n!}B_{n-1}(an)$ to integral using $B_n(x)=\frac{n!}{2\pi i}\oint\frac{e^{x(e^t-1)}}{t^{n+1}}dt$

Evaluate $\frac{d^{n-1}}{dw^{n-1}}\csc^{-1}(w)^n$ or $\frac{d^{n-1}}{dw^{n-1}}\left(\frac{\sqrt{w^2-1}+i}w-1\right)^m$

Study number of complex zeros of a function contained in a strip

Can anyone enlighten me on $e^{-x} = \alpha x$

Find $\int_0^\frac\pi2e^{i(ut+v\cos(t))}dt$ or $\int_0^\frac\pi2\sin(w+ut+v\cos(t))dt$ to invert $\frac{\sin(x)}x$

Exact solution to the the equation $(2 \pi - \theta)\cos \theta + \sin \theta = 0$

How can we find Lambert W solution to $\dfrac {x\ln x}{\ln x+1}=\dfrac{e}{2}$?

Solving $\frac{8^x-2^x}{6^x-3^x}=2$

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