132拉普拉斯变换的基本性质 1线性性质 若Lf(t)=F1(S),</t川=F2(S) 则2[A,f(t)+A2f(t力小=A.2Lx+A2[( =A1F1(S)+A2F2(S) 证:[A,f()+A2f2(t)=「[Af(t)+Ayd A,f(t)e dt+a2f2(t)e dt A1F1(S)+A2F2(S) “理形步文通大浮13.2 拉普拉斯变换的基本性质 1.线性性质  f (t ) f (t )e dt −s t  =  + 0 A1 1 A2 2 f (t )e dt f (t )e dt s t −s t  −  =  + 0 2 2 0 A1 1 A F ( S ) F ( S ) = A1 1 + A2 2 F ( S ) F ( S ) = A1 1 + A2 2 f (t ) F ( S ) f (t ) F ( S ) 1 1 2 2 若 [ ]= , [ ]=  f (t ) f (t ) A1 1 A2 2 则 + f (t ) f (t ) 1 1 2 2 = A + A  f (t ) f (t ) A1 1 A2 2 证： +