Question

Wronskian and Linear Independence

score 71 · Answer 1 · 2020-10-28 17:11:00

71

Views

Wronskian and Linear Independence

Published on 28 Oct 2020 - 17:11

score 616 · Answer 2 · 2020-11-12 16:58:42

616

Views

$y_1(t) = t^2$ and $y_2(t) = t|t|$ linearly independent on [-1,1]

Published on 12 Nov 2020 - 16:58

score 953 · Answer 3 · 2020-11-12 18:55:08

953

Views

If $y_1$ and $y_2$ fundamental set of solutions, then no common point of inflection, unless $p(t)$ and $q(t)$ vanish simultaneous there

Published on 12 Nov 2020 - 18:55

score 1.2k · Answer 4 · 2020-11-12 20:58:17

1.2k

Views

For fundamental solutions $y_1,y_2$, there exist one and only one zero of $y_1$ between consecutive zeros of $y_2$.

Published on 12 Nov 2020 - 20:58

score 70 · Answer 5 · 2020-11-13 17:38:09

70

Views

Showing that $y_2$ is a constant multiple of $y_1$ if Wronskian $W[y_1,y_2](t^)=0$ and $y_1(t^)=0$.

Published on 13 Nov 2020 - 17:38

score 88 · Answer 6 · 2020-11-16 06:42:32

88

Views

How does PatrickJMT do variation of parameters without the Wronskian?

Published on 16 Nov 2020 - 6:42

score 1k · Answer 7 · 2020-11-19 07:01:36

1k

Views

Finding one solution of second order DE using another solution using Wronskian

Published on 19 Nov 2020 - 7:01

score 171 · Answer 8 · 2020-12-06 03:55:29

171

Views

Why is $1,x,x^2,x^3,\cdots$ a bad basis?

Published on 06 Dec 2020 - 3:55

score 320 · Answer 9 · 2020-12-12 13:12:07

320

Views

using Liouville-Ostrogradsky to solve differential equation

Published on 12 Dec 2020 - 13:12

score 66 · Answer 10 · 2020-12-13 04:24:21

66

Views

How did $e^x$ get equal to $e^{2x}$?

Published on 13 Dec 2020 - 4:24

score 61 · Answer 11 · 2021-01-02 19:15:17

61

Views

Fundamental system to a differential equation with constant Wronskian

Published on 02 Jan 2021 - 19:15

score 60 · Answer 12 · 2021-01-07 17:59:36

60

Views

Solving this Differential equation.

Published on 07 Jan 2021 - 17:59

score 240 · Answer 13 · 2021-01-08 08:22:47

240

Views

Stability of Solutions to Linear ODE

Published on 08 Jan 2021 - 8:22

score 330 · Answer 14 · 2021-01-25 17:59:48

330

Views

Variation of Parameters to solve

Published on 25 Jan 2021 - 17:59

score 32 · Answer 15 · 2021-02-25 22:30:15

32

Views

Find two LI continuous differentiable functions $f,g: I \in \mathbb{R} \rightarrow \mathbb{R}$ such that $(f\cdot g')(t) - (f'\cdot g)(t)) = 0$.

Published on 25 Feb 2021 - 22:30

List Question

Wronskian and Linear Independence

$y_1(t) = t^2$ and $y_2(t) = t|t|$ linearly independent on [-1,1]

If $y_1$ and $y_2$ fundamental set of solutions, then no common point of inflection, unless $p(t)$ and $q(t)$ vanish simultaneous there

For fundamental solutions $y_1,y_2$, there exist one and only one zero of $y_1$ between consecutive zeros of $y_2$.

Showing that $y_2$ is a constant multiple of $y_1$ if Wronskian $W[y_1,y_2](t^)=0$ and $y_1(t^)=0$.

How does PatrickJMT do variation of parameters without the Wronskian?

Finding one solution of second order DE using another solution using Wronskian

Why is $1,x,x^2,x^3,\cdots$ a bad basis?

using Liouville-Ostrogradsky to solve differential equation

How did $e^x$ get equal to $e^{2x}$?

Fundamental system to a differential equation with constant Wronskian

Solving this Differential equation.

Stability of Solutions to Linear ODE

Variation of Parameters to solve

Find two LI continuous differentiable functions $f,g: I \in \mathbb{R} \rightarrow \mathbb{R}$ such that $(f\cdot g')(t) - (f'\cdot g)(t)) = 0$.

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