昭平中学校庆:求解这个微分方程 :y'=f(x)+g(x)y^2
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y'^2 +yy" = 1,
1.(yy')'= 1,
==>yy'=C1+x,
==>ydy=(C1+x)dx,
==>y^2=C2*x+C3+x^2.
2)C3=1,==>2yy'=C2+2x.
==>C2=-2.
y^2=x^2-2x+1.
3)齐解:y'^2 +yy" = 0,
==>.(yy')'= 0,
==>yy'=C1,
==>ydy=C1dx,
==>y^2=c2*x+c1.