y = Cx^2 + x (1)
y' = 2Cx+1 (2)
y'' = 2C (3)
from (2)
(y')^2 = 4C^2x^2+ 4Cx + 1
= 4C(Cx^2+x) +1
= 2y''y+1
Cx^2+x为通解的微分方程是
2y''y-(y')^2 +1 =0
y
=
Cx^2
+
x
(1)
y'
=
2Cx+1
(2)
y''
=
2C
(3)
from
(2)
(y')^2
=
4C^2x^2+
4Cx
+
1
=
4C(Cx^2+x)
+1
=
2y''y+1
Cx^2+x为通解的微分方程是
2y''y-(y')^2
+1
=0
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