Prove that L[xf(x)]=-(d tilde f(s))/(dt)

emmostatwf 2022-09-06 Answered
Prove that L [ x f ( x ) ] = d f ~ ( s ) d t
my try
By definition
L [ x ( f ( x ) ] = 0 x f ( x ) e s x d x = [ x f ( x ) e s x d x ] 0 0 f ( x ) e s x d x
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Answers (1)

Quinn Alvarez
Answered 2022-09-07 Author has 13 answers
d d s L [ f ( x ) ] = d d s 0 + f ( x ) e s x d x
d d s L [ f ( x ) ] = 0 + f ( x ) d d s ( e s x ) d x
and
d d s ( e s x ) = x e s x
d d s L [ f ( x ) ] = 0 + f ( x ) x e s x d x
d d s L [ f ( x ) ] ( s ) = L [ x f ( x ) ] ( s )
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