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Консультация № 132282
15.04.2008, 10:47
0.00 руб.
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1
1
Помогите решить задачу.
Дана функция z= y^23x - arcsin(xy). Показать что
x^2 dzdx-xy dzdy+y^2=0
Дана функция z= y^23x - arcsin(xy). Показать что
x^2 dzdx-xy dzdy+y^2=0
Обсуждение
Неизвестный
15.04.2008, 11:54
общий
это ответ
Здравствуйте, Kiselev!
z= y^2\3x - arcsin(xy)
Найдем частные производные данной функции:
dz/dx=-y^2/(3*x^2) - y/sqrt(1-x^2*y^2)
dz/dy=2y/(3x) - x/sqrt(1-x^2*y^2)
x^2 dz\dx-xy dz\dy+y^2=
=x^2*(-y^2/(3*x^2) - y/sqrt(1-x^2*y^2)) - xy*(2y/(3x) - x/sqrt(1-x^2*y^2)) + y^2=
=-(y^2)/3 - x^2*y/sqrt(1-x^2*y^2) -2y^2/3 +x^2*y/sqrt(1-x^2*y^2)+y^2=
=-3(y^2)/3+y^2=-y^2+y^2=0
z= y^2\3x - arcsin(xy)
Найдем частные производные данной функции:
dz/dx=-y^2/(3*x^2) - y/sqrt(1-x^2*y^2)
dz/dy=2y/(3x) - x/sqrt(1-x^2*y^2)
x^2 dz\dx-xy dz\dy+y^2=
=x^2*(-y^2/(3*x^2) - y/sqrt(1-x^2*y^2)) - xy*(2y/(3x) - x/sqrt(1-x^2*y^2)) + y^2=
=-(y^2)/3 - x^2*y/sqrt(1-x^2*y^2) -2y^2/3 +x^2*y/sqrt(1-x^2*y^2)+y^2=
=-3(y^2)/3+y^2=-y^2+y^2=0
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