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Консультация № 198716
25.05.2020, 12:10
0.00 руб.
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Уважаемые эксперты! Пожалуйста, помогите определить тип ДУ в : 1) xy'=y-xe^(y/x) ; 2) (x+y-2)dx+(2y-x+4)dy=0 ; 3) y''=(3/x^2)+xe^x ; 4) (y'')^2=y' ; 5) yy''-(y')^2=0 ; 6) (y^3)*y''=-1
Обсуждение
29.05.2020, 19:11
общий
это ответ
Здравствуйте, rrrecord!
1) Уравнение можно преобразовать как
то есть к виду
следовательно, это однородное уравнение первого порядка;
2) Уравнение вида
для которого
называется уравнением в полных дифференциалах. В данном случае M(x,y) = x+y-2, N(x,y) = 2y-x+4 и
то есть это как раз такой случай;
3) Уравнение вида
(в данном случае n = 2 и f(x) = 3/x[sup]2[/sup] + xe[sup]x[/sup]) относится к категории уравнений n-го порядка, допускающих понижение порядка;
4-6) Уравнения вида
или
(не содержащие в явном виде y или x) также допускают понижение порядка путём замены y' = p(x) или y' = p(y) соответственно.
1) Уравнение можно преобразовать как
то есть к виду
следовательно, это однородное уравнение первого порядка;
2) Уравнение вида
для которого
называется уравнением в полных дифференциалах. В данном случае M(x,y) = x+y-2, N(x,y) = 2y-x+4 и
то есть это как раз такой случай;
3) Уравнение вида
(в данном случае n = 2 и f(x) = 3/x[sup]2[/sup] + xe[sup]x[/sup]) относится к категории уравнений n-го порядка, допускающих понижение порядка;
4-6) Уравнения вида
или
(не содержащие в явном виде y или x) также допускают понижение порядка путём замены y' = p(x) или y' = p(y) соответственно.
Форма ответа
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