inverselaplace 1/((s-4)^2)

解答

的拉普拉斯逆变换

\frac{1}{( s - 4 ) ^{2}}

e^{4 t} t

求解步骤

L^{- 1} {\frac{1}{( s - 4 ) ^{2}}}

应用逆变换法则: if

L^{- 1} {F (s)} = f (t)

则

L^{- 1} {F (s - a)} = e^{a t} f (t)

对于

\frac{1}{( s - 4 ) ^{2}} : a = 4, F (s) = \frac{1}{s ^{2}}

= e^{4 t} L^{- 1} {\frac{1}{s ^{2}}}

L^{- 1} {\frac{1}{s ^{2}}} : t

= e^{4 t} t