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Консультация № 186954
17.12.2012, 00:57
90.09 руб.
0
3
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Решить задачу Коши для линейного уравнения второго порядка.
Решить задачу Коши для линейного уравнения второго порядка.
Обсуждение
17.12.2012, 01:40
общий
это ответ
Здравствуйте, roover!
Характеристическое уравнение
имеет корни -1 и -5, следовательно решение однородного уравнения:
Частное решение неоднородного уравнения ищем в виде:
Подставив в уравнение, получим:
A-12B=1
B+12A=0
-4C-18D=0
-4D+18C=1
Отсюда A=1/145; B=-12/145; C=9/170; D=-1/85
Общее решение неоднородного уравнения:
C1=3/40; C2=77/3944.
Ответ:
Характеристическое уравнение
имеет корни -1 и -5, следовательно решение однородного уравнения:
Частное решение неоднородного уравнения ищем в виде:
Подставив в уравнение, получим:
A-12B=1
B+12A=0
-4C-18D=0
-4D+18C=1
Отсюда A=1/145; B=-12/145; C=9/170; D=-1/85
Общее решение неоднородного уравнения:
C1=3/40; C2=77/3944.
Ответ:
4
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