黎卡提方程的两种变换

Two Types Transformation of Riccati Equation

将黎卡提方程dy/dx+ay2=bxmm=0,-2,-4k/2k+1,-k4/2k-1,(k=1,2,…),通过适当的变换化为变量分离的方程;将黎卡提方程dy/dx=p(x)y2+q(x)y+r(x),通过适当的变换化为u'=r2+f(x)的形式。

Riccati equation dy/dx＋ay^2=bxmm=0,-2,-4k/2k-1,-4k/2k-1,（k=1,2,…）can be turn into variable to separate equation through proper transition. Riccati equation dy/dx=p（x）y^2＋q（x）y＋r（x） can be turn into u=r^2＋f（x） through proper transition.