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Консультация № 169998
29.06.2009, 15:01
0.00 руб.
0
1
1
Помогите решить диф. уравнение 2 порядка.
Приложение:
y”+8y’+25y=0
Приложение:
y”+8y’+25y=0
Обсуждение
Неизвестный
29.06.2009, 19:15
общий
это ответ
Здравствуйте, Якупов Ринат Ильдарович.
Решаем с помощью характерестического уравнения : y->1 , y'->k , y"->k^2 .
(k^2)+8*k+25=0 .
Решаем полученое уравнение как обычное квадратное . Находим дискриминант D .
D=(b^2)-4*a*c=64-4*25=64-100=-36 => sqrtD=6*i , i - комплексное число равное корню квадратному из (-1) .
k1,2=(-b+-sqrtD)/(2*a)=(-8+-6*i)/(2*1) => { k1=-4+3i ; k2=-4-3i } .
Теперь по найденым корням характерестического уравнения легкро определяем ешение исходного дифференциального уравнения 2 порядка .
Y(x)=(C1*cos3x+C2*sin3x)*exp(-4*x) .
C1 , C2 -> const ; exp(-4x) - число е в степени (-4х) .
Решаем с помощью характерестического уравнения : y->1 , y'->k , y"->k^2 .
(k^2)+8*k+25=0 .
Решаем полученое уравнение как обычное квадратное . Находим дискриминант D .
D=(b^2)-4*a*c=64-4*25=64-100=-36 => sqrtD=6*i , i - комплексное число равное корню квадратному из (-1) .
k1,2=(-b+-sqrtD)/(2*a)=(-8+-6*i)/(2*1) => { k1=-4+3i ; k2=-4-3i } .
Теперь по найденым корням характерестического уравнения легкро определяем ешение исходного дифференциального уравнения 2 порядка .
Y(x)=(C1*cos3x+C2*sin3x)*exp(-4*x) .
C1 , C2 -> const ; exp(-4x) - число е в степени (-4х) .
5
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