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Консультация № 165264
18.04.2009, 10:04
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Здравствуйте уважаемые эксперты! Помогите пожалуйста решить одно из линейных неоднородных уравнений, не могу никак понять каким образом это нужно делать.
y''''-6*y'''-6=0.
Замечание: в примере, вместо черырех штрихов нарисано "IV" как степень, я подумала, что это может быть опечатка, потому написала четыре штриха.
Благодарю за внимание!
y''''-6*y'''-6=0.
Замечание: в примере, вместо черырех штрихов нарисано "IV" как степень, я подумала, что это может быть опечатка, потому написала четыре штриха.
Благодарю за внимание!
Обсуждение
18.04.2009, 11:40
общий
это ответ
Здравствуйте, Cassie!
IV - это не опечатка, так тоже обозначают четвертую производную.
В результате замены z=y'''уравнение перепишется в виде:
z'-6z-6=0.
Это уравнение можно решить либо методом разделения переменных, либо найти решение в виде суммы общего решения однородного уравнения и любого частного решения неоднородного. У Вас должно получится:
z(x)=-1+C*exp(6x).
Теперь найдем y(x), последовательно инегрируя z(x):
y(x)=C1+C2*x+C3*x^2-1/6*x^3+C*exp(6*x).
IV - это не опечатка, так тоже обозначают четвертую производную.
В результате замены z=y'''уравнение перепишется в виде:
z'-6z-6=0.
Это уравнение можно решить либо методом разделения переменных, либо найти решение в виде суммы общего решения однородного уравнения и любого частного решения неоднородного. У Вас должно получится:
z(x)=-1+C*exp(6x).
Теперь найдем y(x), последовательно инегрируя z(x):
y(x)=C1+C2*x+C3*x^2-1/6*x^3+C*exp(6*x).
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