미분 방정식 y*y'-(y)^2-y^2*y'=0

미분 방정식 y*y'-(y)^2-y^2*y'=0

yy''-y'^2=y^2y'
(yy''-y'^2)/y^2=y'
(y'/y)'=y'
양쪽 포인트:y'/y=y+C1
dy/dx=y^2+C1y
dy/[y(y+C1)]=dx
양쪽 포인트,
왼쪽=1/C1∫(1/y-1/(y+C1)dy=1/C1ln|y/(y+C1)|+C2
오른쪽=x+C2
그래서 1/C1ln|y/(y+C1)|=x+C2
ln|y/(y+C1)|=C1x+C2
y/(y+C1)=C2e^(C1x)
y=C1C2e^(C1x)/(1-C2e^(C1x))