List questions from singular-solution

Published on 07 Mar 2022 - 6:44

191

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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 23 Feb 2026 - 6:25

141

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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 23 Feb 2026 - 6:25

129

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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 23 Feb 2026 - 6:25

92

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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 23 Feb 2026 - 6:25

94

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Frobenius method solution

Published on 02 May 2022 - 9:19

176

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How to find the singular solution of this DE?

Published on 05 May 2022 - 6:24

645

Views

Singular solution of differential equation $p^2y+2px-y=0$

Published on 15 May 2022 - 12:50

816

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

Published on 23 Feb 2026 - 6:19

55

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quasi-solvable ode

Published on 11 Sep 2022 - 17:08

148

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Prove only 1 solution exists for the following equation $x^2 = y^2 + 71$ where $x, y$ and pos integers

Published on 08 Nov 2022 - 1:04

212

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

Published on 23 Feb 2026 - 6:24

49

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How to find singular solutions from a general one

Published on 18 Dec 2022 - 13:14

32

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What is the general solution ( without start terms ) of laplace equation - $u_{ss}=-u_{tt}$

Published on 13 Jan 2023 - 19:46

List Question

On the existence of singular solution for an ODE

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)

Frobenius method solution

How to find the singular solution of this DE?

Singular solution of differential equation $p^2y+2px-y=0$

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

quasi-solvable ode

Prove only 1 solution exists for the following equation $x^2 = y^2 + 71$ where $x, y$ and pos integers

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

How to find singular solutions from a general one

What is the general solution ( without start terms ) of laplace equation - $u_{ss}=-u_{tt}$

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