Question

以函数y=Cx^2+x为通解的微分方程是____

Answer 1

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