一道高数(微分方程)的题目!

问题描述:

一道高数(微分方程)的题目!
已知微分方程dy/dx+p(x)y=f(x).
有两个特解y1=-1/4x^2 y2=-1/4x^2-4/(x^2)
求满足的p(x),f(x),并给出方程通解.
key:
2/x
-x
C4/(x^2)-1/4x^2

(y1)'=(1/4x^2)'=1/2*x(y2)'=-1/2*x+8/(x^3)将y1 y2 和(y1)’ (y2)'代入微分方程,得-1/2*x-1/4*x^2*p(x)=f(x) (1)-1/2*x+8/(x^3)-1/4x^2 p(x)+4/(x^2) p(x)=f(x) (2)两式相减,得4/x^2 *p(x)=8/x^3于是p(x...