齐次对应的特征方程r^2+2r+3=0r=(-2±2√2)/2=-1±√2所以齐次通解为y=e^(-x)[cos(√2x)+sin(√2x)]设特解是y=ax^2+bx+cy'=2ax+by''=2a代入原方程得2a+2(2ax+b)+3(ax^2+bx+c)=3x-1用待定系数法得3a=0,4a+3b=3,2a+2b+...