求解微分方程 dy/dx-y=x*y^3 的解

令 u = y^(1-3) = y^(-2)
du = -2y^(-3) dy
dy/dx - y = x*y^3
dy/(y^3) dx - y^(-2) = x
-0.5 du/dx - u = x
du/dx + 2u = -2x
(e^(2x)u)' = -2e^(2x)x
e^(2x)u = -2([x*e^(2x)]/2 - [e^(2x)]/4 + C)
y^(-2)代回u
可以解出y,因为过于繁琐,所以不在做化简

对于
dy/dx + P(x)y = Q(x)y^n (Bernoulli differential equation)
令u = y^(1-n)
解得
du/dx + (1-n)P(x)u = (1-n)Q(x)
即线性微分方程,十分简便