y'-xy'=2(y^2+y') 求通解或特解

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y''-xy''=2(y^2+y'')求通解或特解y''-xy''=2(y^2+y'')求通解或特解y''-xy''=2(y^2+y'')求通解或特解∵y''-xy''=2(y²+y'')==>y''-xy''=2y&

y'-xy'=2(y^2+y') 求通解或特解
y'-xy'=2(y^2+y') 求通解或特解

y'-xy'=2(y^2+y') 求通解或特解
∵y'-xy'=2(y²+y') ==>y'-xy'=2y²+2y'
==>(x+1)y'=-2y²
==>dy/y²=-2dx/(x+1)
==>1/y=2ln│x+1│+ln│C│ (C是非零积分常数)
==>e^(1/y)=C(x+1)²
∴原方程的通解是e^(1/y)=C(x+1)² (C是非零积分常数).

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