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jahbreingram123
10.09.2021 •
Mathematics
F(x)=x^2. What is g(x)?
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Ответ:
y = e^(2x) cos 3x is a explicit solution of y'' − 4y' + 13y = 0
Step-by-step explanation:
y'' − 4y' + 13y = 0 (1)
Verify that y = e^(2x) cos 3x is a explicit solution. We derive this solution:
y'=2e^(2x) cos 3x-3e^(2x) sin 3x (2)
y''=4e^(2x) cos 3x - 6e^(2x) sin 3x -6e^(2x) sin 3x -9e^(2x) cos 3x
y''=-5e^(2x) cos 3x - 12e^(2x) sin 3x (3)
In order to verify, we replace (2) (3) in (1):