求方程Dy/Dx=y(y-1),y(0)=1的解

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求方程Dy/Dx=y(y-1),y(0)=1的解求方程Dy/Dx=y(y-1),y(0)=1的解求方程Dy/Dx=y(y-1),y(0)=1的解dy/【y(y-1)】=dxdy/(y-1)-dy/y=

求方程Dy/Dx=y(y-1),y(0)=1的解
求方程Dy/Dx=y(y-1),y(0)=1的解

求方程Dy/Dx=y(y-1),y(0)=1的解
dy/【y(y-1)】 = dx
dy/(y-1) - dy/y = dx
d(y-1)/(y-1) - dy/y = 1·dx
ln/ (y-1)/y / = x + C ,代入x = 0 ,y = 1 ,得:
C = 0 ,解为 y = 1 + y·e^x