再论几类一阶常微分方程的可积判据

On integral criteria of some kinds of first-order differential equations

提出几类一阶常微分方程 ,通过变量替换法化为齐次微分方程 ,再借助交换变量位置法 ,论证它们的可积判据 ,给出它们通积分的表达式 ,所得结果是相应文献结果的推广 .

This paper puts forth some kinds of first-order differential equations, which are transformed into homogeneous differential equations. It proves their integral criteria and gives their expversion of integral by substitution of variables position method.Thus expancling their scope of uses.