以函数y=Cx^2+x为通解的微分方程是____
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以函数y=Cx^2+x为通解的微分方程是____
![以函数y=Cx^2+x为通解的微分方程是____](/uploads/image/z/5225763-3-3.jpg?t=%E4%BB%A5%E5%87%BD%E6%95%B0y%3DCx%5E2%2Bx%E4%B8%BA%E9%80%9A%E8%A7%A3%E7%9A%84%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E6%98%AF____)
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
再问: 不对,这是一阶微分方程
再答: 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为通解的微分方程是 y=xy'
再问: 还是不对
再答: 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为通解的微分方程是 2y = x(y'+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
再问: 不对,这是一阶微分方程
再答: 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为通解的微分方程是 y=xy'
再问: 还是不对
再答: 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为通解的微分方程是 2y = x(y'+1)