正解例

1. 
   
   $$\mbox{$\cal L$}\left[4f(x)-\frac{5}{3}g(x)\right](s) =4\mb... ...)-\frac{5}{3}\mbox{$\cal L$}[g(x)](s) =4F(s)-\frac{5}{3}G(s)$$
   
   

2. $$\begin{eqnarray*} \lefteqn{\mbox{$\cal L$}\left[2f\left(\frac{x}{2}\right)-\mbo... ...[f(x)]\left(\frac{s}{a}\right) \right)\\ & = & 4F(2s)-G(s-3) \end{eqnarray*}$$
   
   
   
   
   

3. $$\begin{eqnarray*} \lefteqn{\mbox{$\cal L$}[\{xf(x)\}'+xg'(x)](s)}\\ & = & \mb... ...[g(x)](s)-g(0)\}\\ & = & -sF'(s)-(sG(s))'=-sF'(s)-G'(s)-sG(s) \end{eqnarray*}$$