Linear algebra – A question to solve a differential equation.

$ mathbf {The Problem is}: $ To let, $ operatorname {u (t) = (u_1 (t), u_2 (t))} $ Where $ t gt 0 $ be the unique solution of the differential equation $
operatorname {du / dt} = Au (t) $
Where $ operatorname {u (0)} = (1,1) $ and $ A = $$
begin {bmatrix}
a & c \
c & b \
end {bmatrix}
$$ is a $
2 ร— 2$ symmetric matrix with $tr A lt 0$ and $ operatorname {det} A gt 0$, then evaluate $lim_ {t to infty} operatorname {u_1 (t)}. $

$ mathbf {my approach} $ : I could only think that by the given information both eigenvalues โ€‹โ€‹of $ A $ are real and negative and therefore $ A ^ (- 1) $ exists and
$$
begin {bmatrix}
operatorname {du_1 (t) / dt} \
operatorname {du_2 (t) / dt} \
end {bmatrix}
=
begin {bmatrix}
au_1 (t) + cu_2 (t) \
cu_1 (t) + bu_2 (t) \
end {bmatrix}
$$
but I can not get any further.

[ Politics ] Unanswered question: Why do Trump supporters have to carry a gun in public, I'm just wearing a small flashlight with a stroke lunette?

[Politics] Open question: Why do Trump supporters have to carry a gun in public, I'm just wearing a small flashlight with a bounce?

Product data – (P2WSH-nestedin-P2SH) Problem solving question 1 + 5 = 6

This is my first question on this platform.

This matter has severely scratched my head, please pay patiently to read my question.

I'm trying to move traditional p2sh tx to p2wsh-nestedin-p2sh tx and this is also an ANYONE_CAN_SPEND tx.

scriptpubkey (hex) = a9149a6185672bafea7a16309a9f6e2fe03927499c6e87

scriptpubkey (asm) = OP_HASH160 9a6185672bafea7a16309a9f6e2fe03927499c6e OP_EQUAL

scriptsig (hex) = 2200201f41c545a5c0b1c370c2e2812b3256d690fc098ae56aa21c94cd98d7c3ca5ec6

p2sh redeemscript (hex) = 00201f41c545a5c0b1c370c2e2812b3256d690fc098ae56aa21c94cd98d7c3ca5ec6

So far as all I mentioned above are simple traditional p2sh lock / unlock, my base serialized tx now shows.

01000000012649c299694db1b608d4463e3b0535b3b8c0d5a1e9558b4d71be3790bde1dce800000000232200201f41c545a5c0b1c370c2e2812b3256d690fc098ae56aa21c94cd98d7c3ca5ec6ffffffff01401f0000000000001976a91451d2a5e04d25ceaa86e600a6ec34bd24431c675d88ac00000000

This is correct because the result generated by https://testnet.smartbit.com.au/txs/pushtx "PUSH TRANSACTION ERROR: 64: NON-MANDATORY-SCRIPT-VERIFY-FLAG (WITNESS PROGRAM PASSED TO EMPTY WITNESS) "indicates.

Next, I will dissolve witness data.

Witnesses Information:

P2WSH-RedeemScript (hex) = 55935687

P2WSH-RedeemScript (asm) = OP_5 OP_ADD OP_6 OP_EQUAL

Witnesses (hex) = 51

Witness objects (asm) = OP_1

The serialized TX looks like this and the bold part is my new change from the previous one.

010000000001012649c299694db1b608d4463e3b0535b3b8c0d5a1e9558b4d71be3790bde1dce800000000232200201f41c545a5c0b1c370c2e2812b3256d690fc098ae56aa21c94cd98d7c3ca5ec6ffffffff01401f0000000000001976a91451d2a5e04d25ceaa86e600a6ec34bd24431c675d88ac020151045593568700000000

when I submit this tx, the error told me "PUSH TRANSACTION ERROR: 64: NON-MANDATORY SCRIPT VERIFY FLAG (SCRIPT EVALUATED WITHOUT ERROR, BUT FINISHED WITH A FALSE / EMPTY TOP STACK ELEMENT)"

I try to solve the puzzle in a magical way and I am successful if I change the script in

010000000001012649c299694db1b608d4463e3b0535b3b8c0d5a1e9558b4d71be3790bde1dce800000000232200201f41c545a5c0b1c370c2e2812b3256d690fc098ae56aa21c94cd98d7c3ca5ec6ffffffff01401f0000000000001976a91451d2a5e04d25ceaa86e600a6ec34bd24431c675d88ac020101045593568700000000

So my last submitted tx show here https://testnet.smartbit.com.au/tx/e627feb66ed572b97ef393f20be0e76edb8dfe34fd98a9c606f62af04496341d

The unformatted text is displayed here: https://api.blockcypher.com/v1/btc/test3/txs/e627feb66ed572b97ef393f20be0e76edb8dfe34fd98a9c606f62af04496341d?limit=50&includeHex=true

I do not understand how it comes that a change solves my math puzzle. ๐Ÿ™

[ Politics ] Open Question: Is not it ironic that Trumpers did not want him imprisoned for his crimes, but spent eight years trying to arrest Obama and Hillary in vain?

[Politics] Open Question: Is not it ironic that Trumpers did not want him imprisoned for his crimes but spent eight years trying to arrest Obama and Hillary for nothing?