Question

y′+y/1-x＝x²-x的通解怎么写？

Answer 1

y′ + y/(1-x) ＝ x²-x 是一阶线性微分方程·， 通解是
y = e^[-∫dx/(1-x)] {∫(x²-x)e^[∫dx/(1-x)]dx + C}
= (x-1){∫[(x²-x)/(x-1)]dx + C} = (x-1)[∫xdx + C] = (x-1)(x^2/2 + C)