题目 Problem Find the particular solution of the differential equation 6d2xdt2+ 3dxdt+6x= e−t,\begin{align*} 6\frac{\mathrm{d}^2x}{\mathrm{d}t^2} +&\, 3\frac{\mathrm{d}x}{\mathrm{d}t} + 6x =&\, e^{-t}, \end{align*}6dt2d2x+3dtdx+6x=e−t, given that, when t=0t = 0t=0, x=dxdt=0x = \frac{\mathrm{d}x}{\mathrm{d}t} = 0x=dtdx=0. [10] 题目中文翻译 求微分方程 6d2xdt2+ 3dxdt+6x= e−t,\begin{align*} 6\frac{\mathrm{d}^2x}{\mathrm{d}t^2} +&\, 3\frac{\mathrm{d}x}{\mathrm{d}t} + 6x =&\, e^{-t}, \end{align*}6dt2d2x+3dtdx+6x=e−t, 的特解，已知当 t=0t = 0t=0 时，x=dxdt=0x = \frac{\mathrm{d}x}{\mathrm{d}t} = 0x=dtdx=0。 解答
