某一阶微分方程

tommywong · 发表于 2014-10-14 10:11

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

战巡 · 发表于 2014-10-16 10:28

\[y'y^{-3}+xy^{-4}=x^2\]
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 · 发表于 2023-4-15 07:36

first-order nonlinear ordinary differential equation

Slope field
Plots of sample individual solution
Sample solution family

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