Question

Linear Independence of n functions - Wronskian help

score 36 · Answer 1 · 2021-03-30 19:28:20

36

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Linear Independence of n functions - Wronskian help

Published on 30 Mar 2021 - 19:28

score 140 · Answer 2 · 2021-04-17 14:37:24

140

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Given $ty'' + 3y' = - te^t$ and $W(y_1,y_2)(1) = 2$ ($y_1$ and $y_2$ are LI solutions) find $W(y_1,y_2)(2)$

Published on 17 Apr 2021 - 14:37

score 124 · Answer 3 · 2021-04-27 01:01:17

124

Views

Using Leibniz rule to prove that a particular solution for the equation $Lx=0$ is given by $x_{p}(t)=\int_{a}^{t}\varphi(t-s)f(s)ds$.

Published on 27 Apr 2021 - 1:01

score 775 · Answer 4 · 2021-04-27 14:35:54

775

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Prove that the Wronskian of a fundamental set of solutions is always non-zero?

Published on 27 Apr 2021 - 14:35

score 197 · Answer 5 · 2021-05-08 00:29:11

197

Views

Why does the Wronskian work?

Published on 08 May 2021 - 0:29

score 73 · Answer 6 · 2021-06-14 16:51:46

73

Views

If $y_1$ and $y_2$ are two special different answers for the equation below, and $y_1=y_2+f(x)$, then how to find $f(x)$?

Published on 14 Jun 2021 - 16:51

score 96 · Answer 7 · 2026-02-23 06:35:03

96

Views

Do irreducible sums span the same space?

Published on 23 Feb 2026 - 6:35

score 1k · Answer 8 · 2021-07-12 13:04:08

1k

Views

Finding the general solution using variation of parameters: $\left(1-x\right)y''+xy'-y=2\left(x-1\right)^2e^{-x}$

Published on 12 Jul 2021 - 13:04

score 97 · Answer 9 · 2021-08-08 17:28:51

97

Views

If the Wronskian $W(y_1,y_2)(0)=1$ then $W(y_1,y_2)(-1)=? $

Published on 08 Aug 2021 - 17:28

score 22 · Answer 10 · 2021-09-03 03:43:21

22

Views

Linear combination of functions and their Wronskian.

Published on 03 Sep 2021 - 3:43

score 53 · Answer 11 · 2021-09-04 20:08:32

53

Views

functions whose Wronskian is zero aren't necessarily dependent

Published on 04 Sep 2021 - 20:08

score 254 · Answer 12 · 2021-09-11 00:52:33

254

Views

Why do we use the function derivatives in the Wronskian?

Published on 11 Sep 2021 - 0:52

score 87 · Answer 13 · 2021-09-18 17:34:35

87

Views

Definition of independent set of functions on an interval

Published on 18 Sep 2021 - 17:34

score 125 · Answer 14 · 2021-09-22 13:50:11

125

Views

Proving $\sin^2(x)+\cos^2(x)=1$ using Abel's Theorem / Deriving Pythagoras Theorem from Abel's Theorem

Published on 22 Sep 2021 - 13:50

score 270 · Answer 15 · 2021-11-05 00:50:09

270

Views

Derivative of the Wronskian

Published on 05 Nov 2021 - 0:50

List Question

Linear Independence of n functions - Wronskian help

Given $ty'' + 3y' = - te^t$ and $W(y_1,y_2)(1) = 2$ ($y_1$ and $y_2$ are LI solutions) find $W(y_1,y_2)(2)$

Using Leibniz rule to prove that a particular solution for the equation $Lx=0$ is given by $x_{p}(t)=\int_{a}^{t}\varphi(t-s)f(s)ds$.

Prove that the Wronskian of a fundamental set of solutions is always non-zero?

Why does the Wronskian work?

If $y_1$ and $y_2$ are two special different answers for the equation below, and $y_1=y_2+f(x)$, then how to find $f(x)$?

Do irreducible sums span the same space?

Finding the general solution using variation of parameters: $\left(1-x\right)y''+xy'-y=2\left(x-1\right)^2e^{-x}$

If the Wronskian $W(y_1,y_2)(0)=1$ then $W(y_1,y_2)(-1)=? $

Linear combination of functions and their Wronskian.

functions whose Wronskian is zero aren't necessarily dependent

Why do we use the function derivatives in the Wronskian?

Definition of independent set of functions on an interval

Proving $\sin^2(x)+\cos^2(x)=1$ using Abel's Theorem / Deriving Pythagoras Theorem from Abel's Theorem

Derivative of the Wronskian

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