解法一：（全微分法） ∵y'-2y/x=x^3 ==>xy'-2y=x^4 ==>xdy-2ydx=x^4dx ==>x²dy-2xydx=x^5dx ==>x²dy-yd(x²)=x^5dx ==>[x²dy-yd(x²)]/x^4=xdx ==>d(y/x²)=d(x²/2) ==>y/x²=x²/2+C (C是积分常数) ==...
任何一个高阶线性微分方程都可以转化成线性微分方程组
xy'-2y=x^4 ==>xdy-2ydx=x^4dx ==>x²dy-2xydx=x^5dx"}}}'>