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Консультация № 178961
06.06.2010, 21:31
0.00 руб.
0
2
2
Здравствуйте. Нужно решить уравнение.
1. y’cosx-2ysinx=2;y0=3;x0=0
1. y’cosx-2ysinx=2;y0=3;x0=0
Обсуждение
Неизвестный
08.06.2010, 10:30
общий
это ответ
Здравствуйте, Ананьев Рудольф Олегович.
y = uv тогда y' = u'v + uv'
u'v + uv'-2uv tgx = 2
для начала решим однородное уравнение
u'v + uv'-2uv tgx = 0
u'v + u(v'-2v tgx) = 2
выберем функцию v такую что v'-2v tgx = 0
ln|v| + 2ln|cosx|= ln|C|
в силу произвольности v возьмем С = 1
v = C cos^2x
в силу произвольности v возьмем С = 1
v = cos^2x
u'cos^2x = 2
u' = 2/cos^2x
u = 2tgx+C
y = uv = (2tgx+C)cos^2x = sin2x+Ccos^2x -общее решение
x0 = 0
y0 = 3
3 = sin20+Ccos^2*0 = 0 + C*1 => C = 3
y = sin2x+3cos^2x - частное решение
y = uv тогда y' = u'v + uv'
u'v + uv'-2uv tgx = 2
для начала решим однородное уравнение
u'v + uv'-2uv tgx = 0
u'v + u(v'-2v tgx) = 2
выберем функцию v такую что v'-2v tgx = 0
ln|v| + 2ln|cosx|= ln|C|
в силу произвольности v возьмем С = 1
v = C cos^2x
в силу произвольности v возьмем С = 1
v = cos^2x
u'cos^2x = 2
u' = 2/cos^2x
u = 2tgx+C
y = uv = (2tgx+C)cos^2x = sin2x+Ccos^2x -общее решение
x0 = 0
y0 = 3
3 = sin20+Ccos^2*0 = 0 + C*1 => C = 3
y = sin2x+3cos^2x - частное решение
5
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