某一阶微分方程

tommywong

$y'+\frac{x}{y}=x^2y^3$

战巡

\[y'y^{-3}+xy^{-4}=x^2\]
令$g=y^{-2}$，有$g'=-2y'y^{-3}$，然后有
\[-\frac{g'}{2}+xg^2=x^2\]
后面的嘛.........自己看吧
http://www.wolframalpha.com/input/?i=DSolve[-g%27[x]%2F2+%2B+x+g[x]^2+%3D%3D+x^2%2C+g[x]%2C+x]%2F%2FFullSimplify

hbghlyj

first-order nonlinear ordinary differential equation

Slope field
Plots of sample individual solution
Sample solution family