重庆交通大学学报（自然科学版） ›› 1985, Vol. 4 ›› Issue (3): 1-12.
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刘成群, 罗诗裕
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Liu Chengqun, Luo Shiyu
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摘要： 本文利用变换Y=ye-v(x,y),dX=eu(x,y)dx将变系数二阶非线性微分方程y"+f(x,y)y'2+φ(x,y)y'+ψ(x,y)=0化为线性方程Y"+b1Y'+b2Y+b3=0并讨论了这种变换的充分必要条件,给出了通解公式,得到了一系列可积的新类型。
Abstract: In this paper, a second order nonlinear differential equation with variable coefficients y"+f(x,y)y'2+φ(x,y)y'+ψ(x,y)=0 was reduced to a linear equation Y"+b2Y'+b2Y+b3=0 by using a transformation Y=ye-v(x,y),dX=eu(x,y)dx; The sufficient and necessary conditions for the transformation were discussed and the formula of the general solution was given. Several kinds integral were obtained.
刘成群, 罗诗裕. 关于一类变系数二阶非线性微分方程的解[J]. 重庆交通大学学报（自然科学版）, 1985, 4(3): 1-12.
Liu Chengqun, Luo Shiyu. On the Solution for a Class of Second Order Nonlinear Ordinary Differential Equation with Variable Coefficients[J]. Journal of Chongqing Jiaotong University(Natural Science), 1985, 4(3): 1-12.
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