解微分方程 y*y''-(y')^2-y^2*y'=0

解微分方程 y*y''-(y')^2-y^2*y'=0

yy''-y'^2=y^2y'
(yy''-y'^2)/y^2=y'
(y'/y)'=y'
兩邊積分：y'/y=y+C1
dy/dx=y^2+C1y
dy/[y(y+C1)]=dx
兩邊積分,
左邊=1/C1∫(1/y-1/(y+C1))dy=1/C1lny/(y+C1)+C2
右邊=x+C2
所以1/C1lny/(y+C1)=x+C2
lny/(y+C1)=C1x+C2
y/(y+C1)=C2e^(C1x)
y=C1C2e^(C1x)/(1-C2e^(C1x))

Elden Ring Premiere

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