(y+1)^2dy/dx+x^2=0求通解过程

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(y+1)^2dy/dx+x^2=0求通解过程(y+1)^2dy/dx+x^2=0求通解过程(y+1)^2dy/dx+x^2=0求通解过程∵(y+1)^2dy/dx+x^2=0,∴(y+1)^2dy=

(y+1)^2dy/dx+x^2=0求通解过程
(y+1)^2dy/dx+x^2=0求通解过程

(y+1)^2dy/dx+x^2=0求通解过程
∵(y+1)^2dy/dx+x^2=0,∴(y+1)^2dy=-x^2dx,∴∫(y+1)^2dy=-∫x^2dx,
∴(1/3)(y+1)^3=-(1/3)x^3+C,∴(y+1)^3=-x^3+C.
∴原微分方程的通解是:(y+1)^3=-x^3+C.