y'-xy'=a(y'+y^2)求通解

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y'-xy'=a(y'+y^2)求通解
y'-xy'=a(y'+y^2)求通解

y'-xy'=a(y'+y^2)求通解
∵y'-xy'=a(y'+y²) ==>(1-a-x)y'=ay²
==>dy/y²=adx/(1-a-x)
==>-1/y=-aln│1-a-x│-ln│C│ (C是积分常数)
==>e^(1/y)=C(1-a-x)^a
∴原方程的通解是e^(1/y)=C(1-a-x)^a (C是积分常数).

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