一类二阶非线性微分方程的可积定理及其应用

Integrable Therom of one Kind of Second-order Nonlinear Differential Equation and It’s Applications

利用一类Riccati方程z′=z2-a(x)z+b(x)的求解公式,给出了一类二阶非线性微分方程的通解,应用这些只与方程系数a(x)与b(x)相关的求解公式,求通解过程十分简捷.

According to the solution of one class Riccati equationsz′=z2-a（x）z＋b（x）,the author considers the general solution of the one class Nonlinear Second Order Differential Equations,The process of using these formulas only with a（x）and b（x）to find the general solution of such differential equations is forthright.