特征方程 r^2+r = 0, r = 0, -1.故设特解 y = (ax^2+bx+c)e^x,则 y' = (ax^2+(b+2a)x+c+b)e^xy'' = (ax^2+(b+4a)x+c+2b+2a)e^x代入微分方程得 2a = 2, 2b+6a = 0, 2c+3b+2a = 0a = 1, b = -3, c = 7/2, 特解 y = (x^2-3x+7/2)e^x通解 y = C1 + C2e^(-x) + (x^2-3x+7/2)e^x