Re: [理工] [工數]-一階ODE
※ 引述《kagato (包)》之銘言：
: [xy(x^2 - y^2)^(1/2) + x]y'=y - x^2 *(x^2 - y^2)^(1/2)
: 拜託版上高手了@@
[ xy √(x^2 - y^2) + x ] dy = [ y - x^2 * √(x^2 - y^2) ] dx
x dy - y dx + x * √(x^2 - y^2) ( x dx + y dy ) = 0
2
x d ( y / x ) + x * √(x^2 - y^2) ( x dx + y dy ) = 0
d ( y / x ) + √( 1 - (y/x)^2) ( x dx + y dy ) = 0
d ( y / x )
----------------- + x dx + y dy = 0
√( 1 - (y/x)^2)
-1 x^2 y^2
sin ( y / x ) + ------ + ------ = c
2 2
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10/12 18:52, , 1F
10/12 18:52, 1F
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