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ÂÞ²®ÌØË÷·Æ: ½ð±Ò+1, ¡ï¡ï¡ïºÜÓаïÖú 2014-05-26 01:55:56
1¡¢a*u'^2=(a+2)*(u*u''+a)  (a¡Ù2)
Áîu'=y,
Ôò u''=dy/dx=dy/du*du/dx=y*dy/du
a*y^2=(a+2)*(u*y*dy/du+a)=(a+2)*[1/2*u*d(y^2)/du+a]
ÔÙÁîV=y^2
dV/du-2*a/[(a+2)*u]*V=-2*a/u
V=u^[2*a/(a+2)]*{C+Integral{[-2*a/u]*u^[-2*a/(a+2)]}*du}
V=C*u^[2*a/(a+2)]+u^[-2*a/(a+2)]
Integral{du/sqrt{1+C*u^[4*a/(a+2)]}}=x+D
2Â¥2014-05-23 14:23:34
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2Â¥: Originally posted by peterflyer at 2014-05-23 14:23:34
1¡¢a*u'^2=(a+2)*(u*u''+a)  (a¡Ù2)
Áîu'=y,
Ôò u''=dy/dx=dy/du*du/dx=y*dy/du
a*y^2=(a+2)*(u*y*dy/du+a)=(a+2)*
ÔÙÁîV=y^2
dV/du-2*a/*V=-2*a/u
V=u^*{C+Integral{*u^}*du}
V=C*u^+u^
Integral{du/sqrt{ ...

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3Â¥: Originally posted by ÂÞ²®ÌØË÷·Æ at 2014-05-25 00:13:14
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