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為通解的微分方程是
2y''y-(y')^2 +1 =0不對，這是一階微分方程y = Cx^2 + x(1)y' = 2Cx+1(2)y'' = 2C (3)from (1)y = Cx^2 + x = x(Cx+1)=xy' Cx^2+x為通解的微分方程是y=xy'還是不對y = Cx^2 + x(1)y' = 2Cx+1(2)y'' = 2C (3)from (1)y = Cx^2 + x = (x/2)((2Cx+1) +1)=(x/2)((y'+1)2y = x(y'+1) Cx^2+x為通解的微分方程是2y = x(y'+1)