4类可化为齐次方程的高次微分方程的求解方法

Solving four classes of high degree differential equations converted into homogeneous equations

根据微分方程dy/dx=a1x+b1y+c1/a2x+b2y+c2的求解方法,对4类具有特定形式的高次微分方程进行了研究,通过变量代换,将其转化为dy/dx=+1x+b1y+c1/a2x+b2y+c2的形式,从而求出其通解.通过实例说明方法的有效性.

Based on the solving method of differential equation dy/dx=a1x＋b1y＋c1/a2x＋b2y＋c2,four classes of high degree differential equations with a specific form are studied.Through variable substitution,they are converted into dy/dx=a1x＋b1y＋c1/a2x＋b2y＋c2,so as to find out the general solution.An example is given to illustrate the effectiveness of the method.