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Консультация № 178958
06.06.2010, 20:46
0.00 руб.
0
2
1
Здравствуйте. Нужно решить уравнение.
Y’’=2(1+y’)1/2; y(0)=5, y’(0)=-1
Y’’=2(1+y’)1/2; y(0)=5, y’(0)=-1
Обсуждение
07.06.2010, 20:58
общий
это ответ
Здравствуйте, Ананьев Рудольф Олегович.
1) Делаем замену z=1+y', получаем уравнение z'=2[$8730$]z. Это уравнение с разделяющимися переменными:
dz/(2[$8730$]z)=dx, [$8730$]z=x+C1, z=(x+C1)2. Возвращаясь к y, получаем
y'=(x+C1)2-1.
Интегируя, находим общее решение
y=(1/3)(x+C1)3-x+C2
2) Подставляя начальные условия, имеем
y(0)=(1/3)C13+C2=5
y'(0)=C12-1=-1
Отсюда находим C1=0, C2=5
Ответ: y=(1/3)x3-x+5
1) Делаем замену z=1+y', получаем уравнение z'=2[$8730$]z. Это уравнение с разделяющимися переменными:
dz/(2[$8730$]z)=dx, [$8730$]z=x+C1, z=(x+C1)2. Возвращаясь к y, получаем
y'=(x+C1)2-1.
Интегируя, находим общее решение
y=(1/3)(x+C1)3-x+C2
2) Подставляя начальные условия, имеем
y(0)=(1/3)C13+C2=5
y'(0)=C12-1=-1
Отсюда находим C1=0, C2=5
Ответ: y=(1/3)x3-x+5
5
Форма ответа
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