Question

What are the solutions for $y(t)\cdot\left(y'(t) + a\right)=-b\sin(t)$?

score 218 · Answer 1 · 2022-01-09 20:09:37

218

Views

What are the solutions for $y(t)\cdot\left(y'(t) + a\right)=-b\sin(t)$?

Published on 09 Jan 2022 - 20:09

score 506 · Answer 2 · 2022-02-14 20:19:20

506

Views

Is the function $f(x)=\frac{\left(1-x^2+\sqrt{\left(1-x^2\right)^2}\right)}{2}e^{-\frac{x^2}{1-x^2}}$ a bump-function $\in C_c^\infty$? Diff. Eq.?

Published on 14 Feb 2022 - 20:19

score 502 · Answer 3 · 2022-02-21 23:50:44

502

Views

Examples of Finite-Duration solutions to Autonomous Ordinary Differential Equations ODEs?

Published on 21 Feb 2022 - 23:50

score 136 · Answer 4 · 2022-02-23 23:46:16

136

Views

Is the rate of change of Finite-Duration Solutions always bounded?

Published on 23 Feb 2022 - 23:46

score 190 · Answer 5 · 2022-03-20 00:24:35

190

Views

Is the solution to $\theta''+0.021\,\text{sgn}(\theta')\sqrt{|\theta'|}+0.02\sin(\theta)=0,\,\theta_0=\pi/2,\,\theta'_0=0$ of finite duration?

Published on 20 Mar 2022 - 0:24

score 140 · Answer 6 · 2022-03-20 02:39:42

140

Views

How to "formally" prove that $x(t)=\frac{1}{4}(2-t)^2\theta(2-t)$ solves $\dot{x}=-\text{sgn}(x)\sqrt{|x|},\,x(0)=1$?

Published on 20 Mar 2022 - 2:39

score 128 · Answer 7 · 2022-03-22 17:44:02

128

Views

Does $x(t) = \exp\left(\frac{t}{t-1}\right)\cdot\theta(1-t)$ solve $\dot{x}\cdot(1-t)^2+x=0,\,\,x(0)=1$?

Published on 22 Mar 2022 - 17:44

score 91 · Answer 8 · 2022-03-31 21:26:03

91

Views

Is $r(t) = \frac{1}{144}(T-t)^4\theta(T-t)$ a valid solution to $\ddot{r}=\sqrt{r},\,r(0)=\frac{T^4}{144}>0$? (with $\theta(t)$ the Heaviside step fn)

Published on 31 Mar 2022 - 21:26

score 265 · Answer 9 · 2022-04-21 23:37:27

265

Views

Does Lipschitz-kind "non-scalar ODEs" and PDEs could stand having finite-duration solutions?

Published on 21 Apr 2022 - 23:37

score 327 · Answer 10 · 2022-05-06 01:43:39

327

Views

Issues with the Fourier Transform of $f(t)=(1-t^2)^4$ on $[-1,\,1]$, should be analytical but looks like having a singularity with noise-like rippling

Published on 06 May 2022 - 1:43

score 815 · Answer 11 · 2022-05-17 04:34:23

815

Views

Are these equations "properly" defined differential equations? (finite duration solutions to diff. eqs.)

Published on 17 May 2022 - 4:34

score 143 · Answer 12 · 2022-05-25 06:45:54

143

Views

Does the Differential Topology/Geometry frameworks being able to model solutions to diff. eqs. that are Non-Smooth?

Published on 25 May 2022 - 6:45

score 147 · Answer 13 · 2022-07-04 00:29:13

147

Views

Find the extinction time $T$ for the solutions $\ddot{y}+a\,\text{sgn}(\dot{y})\sqrt{|\dot{y}|}(1+|\dot{y}|^{3/2})+b\,\sin(y)=0,\,y(0)>0,\,y'(0)=0$?

Published on 04 Jul 2022 - 0:29

score 150 · Answer 14 · 2022-07-25 17:52:06

150

Views

Confusion with the Fourier Transform and Complex Differentiability: example with compact-supported function

Published on 25 Jul 2022 - 17:52

score 211 · Answer 15 · 2022-11-22 20:35:21

211

Views

Proving that these solutions are formally solving these differential equations: $x'' = -\text{sgn}(x')$ and $y'' = \sqrt{|y'|}$

Published on 22 Nov 2022 - 20:35

List Question

What are the solutions for $y(t)\cdot\left(y'(t) + a\right)=-b\sin(t)$?

Is the function $f(x)=\frac{\left(1-x^2+\sqrt{\left(1-x^2\right)^2}\right)}{2}e^{-\frac{x^2}{1-x^2}}$ a bump-function $\in C_c^\infty$? Diff. Eq.?

Examples of Finite-Duration solutions to Autonomous Ordinary Differential Equations ODEs?

Is the rate of change of Finite-Duration Solutions always bounded?

Is the solution to $\theta''+0.021\,\text{sgn}(\theta')\sqrt{|\theta'|}+0.02\sin(\theta)=0,\,\theta_0=\pi/2,\,\theta'_0=0$ of finite duration?

How to "formally" prove that $x(t)=\frac{1}{4}(2-t)^2\theta(2-t)$ solves $\dot{x}=-\text{sgn}(x)\sqrt{|x|},\,x(0)=1$?

Does $x(t) = \exp\left(\frac{t}{t-1}\right)\cdot\theta(1-t)$ solve $\dot{x}\cdot(1-t)^2+x=0,\,\,x(0)=1$?

Is $r(t) = \frac{1}{144}(T-t)^4\theta(T-t)$ a valid solution to $\ddot{r}=\sqrt{r},\,r(0)=\frac{T^4}{144}>0$? (with $\theta(t)$ the Heaviside step fn)

Does Lipschitz-kind "non-scalar ODEs" and PDEs could stand having finite-duration solutions?

Issues with the Fourier Transform of $f(t)=(1-t^2)^4$ on $[-1,\,1]$, should be analytical but looks like having a singularity with noise-like rippling

Are these equations "properly" defined differential equations? (finite duration solutions to diff. eqs.)

Does the Differential Topology/Geometry frameworks being able to model solutions to diff. eqs. that are Non-Smooth?

Find the extinction time $T$ for the solutions $\ddot{y}+a\,\text{sgn}(\dot{y})\sqrt{|\dot{y}|}(1+|\dot{y}|^{3/2})+b\,\sin(y)=0,\,y(0)>0,\,y'(0)=0$?

Confusion with the Fourier Transform and Complex Differentiability: example with compact-supported function

Proving that these solutions are formally solving these differential equations: $x'' = -\text{sgn}(x')$ and $y'' = \sqrt{|y'|}$

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