using the substitution y=ux,find the general solution of (x^2)y*dy/dx=x^3+(x^2)y-y^3用y=ux解微分方程
问题描述：
using the substitution y=ux,find the general solution of (x^2)y*dy/dx=x^3+(x^2)y-y^3
用y=ux解微分方程
答
(x^2)y dy/dx=x^3+(x^2y)-y^3y=ux dy=udx+xdu(x^2)ux*(udx+xdu)=(x^3+x^3u-x^3u^3)dxx^4udu=x^3(1+u-u^2-u^3)dxudu/(1+u-u^2-u^3)=dx/xgeneral solution(1/4)ln[|1+u|/|1-u|] +(1/2)*(1/(1+u))+C=ln|x|