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=e^u(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.

摘要： 本文利用变换Y=ye^-v(x,y),dX=e^u(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。