Question

求解一阶线性微分方程y′-2/x*y=x^3

Answer 1

两边同除以x^2

y'/(x^2)-(2/x^3)y=x

通分

(xy'-2y)/(x^3)=x

[y/(x^2)]'=x

积分

y/(x^2)=(1/2)x^2+C

y=(1/2)x^4+Cx^2