List questions from initial-value-problems

Published on 19 Apr 2022 - 14:56

59

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If an ODE depends on $f \in C^{\infty}(I, \mathbb{R})$ but not on $f'$, does the same hold for its solution?

Published on 21 Apr 2022 - 8:28

37

Views

Solving a PDE with a positively valued characteristic coefficient

Published on 21 Apr 2022 - 10:27

266

Views

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

Published on 23 Feb 2026 - 6:22

40

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Solution of IVP is defined for all $t\in\mathbb{R}$ if $f$ is Lipschitz

Published on 02 May 2022 - 0:32

80

Views

Find initial value $x_0$ in the PDE: $u_t(x,t) + \partial_x \big(a(x,t)\cdot u(x,t)\big) = 0$ when using methods of characteristic

Published on 28 Mar 2026 - 3:27

22

Views

An inequality for a maximal solution of an IVP

Published on 24 May 2022 - 6:55

108

Views

Is the Game of Life predictable?

Published on 23 Feb 2026 - 13:26

23

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Maximal interval where the ODE has unique solution.

Published on 08 Jun 2022 - 17:43

74

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Is 2-Lipschitz the exponential of bounded 2-Lipschitz function?

Published on 09 Jun 2022 - 8:16

33

Views

Solving DE with substitution given the initial values

Published on 09 Jun 2022 - 11:54

61

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Why the solution of the following IVP is the trivial solution?

Published on 15 Jun 2022 - 18:24

629

Views

On the existence of infinitely many linearly independent solutions for a non-linear IVP $y'=f(t,y),~y(t_0)=y_0$.

Published on 16 Jun 2022 - 13:01

52

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Lipschitz continuity and and initial condition problem

Published on 22 Jun 2022 - 20:40

84

Views

$y''+y=x^2+1, y(\pi)=\pi^2, y'(\pi)=2\pi$ - By Laplace Transform

Published on 30 Jun 2022 - 20:48

List Question

Solving the initial value problem as a vector function r(t) from t

If an ODE depends on $f \in C^{\infty}(I, \mathbb{R})$ but not on $f'$, does the same hold for its solution?

Solving a PDE with a positively valued characteristic coefficient

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

Solution of IVP is defined for all $t\in\mathbb{R}$ if $f$ is Lipschitz

Find initial value $x_0$ in the PDE: $u_t(x,t) + \partial_x \big(a(x,t)\cdot u(x,t)\big) = 0$ when using methods of characteristic

An inequality for a maximal solution of an IVP

Is the Game of Life predictable?

Maximal interval where the ODE has unique solution.

Is 2-Lipschitz the exponential of bounded 2-Lipschitz function?

Solving DE with substitution given the initial values

Why the solution of the following IVP is the trivial solution?

On the existence of infinitely many linearly independent solutions for a non-linear IVP $y'=f(t,y),~y(t_0)=y_0$.

Lipschitz continuity and and initial condition problem

$y''+y=x^2+1, y(\pi)=\pi^2, y'(\pi)=2\pi$ - By Laplace Transform

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