Arbitrary constants of 2nd order linear ODE with negative discriminant are complex conjugates?
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I'm in a mathematical modeling course. My professor was showing us how to solve initial value problems regarding 2nd order linear ODEs with a negative discriminant. He asserted that the arbitrary constants of such a solution must be complex conjugates. A link to his notes can be found here: https://drive.google.com/file/d/15-JEfxYYAzie-DKKZ2LXJBhK3QBR0dUe/view?usp=sharing
Skip to page 9. He makes the assertion on page 11.
Can anyone produce a proof of this fact? He threw it straight out of the blue in the lecture.
differential-equations complex-numbers
asked Nov 17 at 14:16
K.defaoite
11
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I'm in a mathematical modeling course. My professor was showing us how to solve initial value problems regarding 2nd order linear ODEs with a negative discriminant. He asserted that the arbitrary constants of such a solution must be complex conjugates. A link to his notes can be found here: https://drive.google.com/file/d/15-JEfxYYAzie-DKKZ2LXJBhK3QBR0dUe/view?usp=sharing
Skip to page 9. He makes the assertion on page 11.
Can anyone produce a proof of this fact? He threw it straight out of the blue in the lecture.
differential-equations complex-numbers
asked Nov 17 at 14:16
K.defaoite
11
Something like this answer? Where exactly do your problems start?
– LutzL
Nov 17 at 14:59
I didn't spot this when I posted the question. Thank you so much!
– K.defaoite
Nov 18 at 12:01
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm in a mathematical modeling course. My professor was showing us how to solve initial value problems regarding 2nd order linear ODEs with a negative discriminant. He asserted that the arbitrary constants of such a solution must be complex conjugates. A link to his notes can be found here: https://drive.google.com/file/d/15-JEfxYYAzie-DKKZ2LXJBhK3QBR0dUe/view?usp=sharing
Skip to page 9. He makes the assertion on page 11.
Can anyone produce a proof of this fact? He threw it straight out of the blue in the lecture.
differential-equations complex-numbers
asked Nov 17 at 14:16
K.defaoite
11
I'm in a mathematical modeling course. My professor was showing us how to solve initial value problems regarding 2nd order linear ODEs with a negative discriminant. He asserted that the arbitrary constants of such a solution must be complex conjugates. A link to his notes can be found here: https://drive.google.com/file/d/15-JEfxYYAzie-DKKZ2LXJBhK3QBR0dUe/view?usp=sharing
Skip to page 9. He makes the assertion on page 11.
Can anyone produce a proof of this fact? He threw it straight out of the blue in the lecture.
differential-equations complex-numbers
differential-equations complex-numbers
asked Nov 17 at 14:16
K.defaoite
11
asked Nov 17 at 14:16
K.defaoite
11
asked Nov 17 at 14:16
K.defaoite
11
asked Nov 17 at 14:16
K.defaoite
11
asked Nov 17 at 14:16
K.defaoite
11
11
Something like this answer? Where exactly do your problems start?
– LutzL
Nov 17 at 14:59
I didn't spot this when I posted the question. Thank you so much!
– K.defaoite
Nov 18 at 12:01
add a comment |
Something like this answer? Where exactly do your problems start?
– LutzL
Nov 17 at 14:59
I didn't spot this when I posted the question. Thank you so much!
– K.defaoite
Nov 18 at 12:01
Something like this answer? Where exactly do your problems start?
– LutzL
Nov 17 at 14:59
Something like this answer? Where exactly do your problems start?
– LutzL
Nov 17 at 14:59
I didn't spot this when I posted the question. Thank you so much!
– K.defaoite
Nov 18 at 12:01
I didn't spot this when I posted the question. Thank you so much!
– K.defaoite
Nov 18 at 12:01
add a comment |
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Something like this answer? Where exactly do your problems start?
– LutzL
Nov 17 at 14:59
I didn't spot this when I posted the question. Thank you so much!
– K.defaoite
Nov 18 at 12:01