12.2 可分离变量的微分方程与一阶线性微分方程

−1 dy
y = f (x),
n
k( n + 1) y = 1,
dx
n−1
∫ k(
n + 1) y dy =
n
∫
dx
y
k( n + 1) ⋅ = x + c,
y( 0) = 0, c = 0
n
n
y(1)
= 1, k =
n + 1
∴ y n = x f n ( x)
= x
Q
f
( x)
≥
0
∴ f ( x)
=
n x