Use Laplace transform to solve xy”+(1−x)y′+my=0

gemuntertjx

gemuntertjx

Answered question

2022-09-05

Use Laplace transform to solve x y + ( 1 x ) y + m y = 0

Answer & Explanation

Kimberly Evans

Kimberly Evans

Beginner2022-09-06Added 13 answers

Hint.
L ( x f ( x ) ) = d d s L ( f ( x ) )
then
d d s L ( y ¨ ) + d d s L ( y ˙ ) + L ( y ˙ ) + m L ( y ) = 0
with
L ( y ¨ ) = s 2 Y ( s ) y ˙ ( 0 ) s y ( 0 ) L ( y ˙ ) = s Y ( s ) y ( 0 )
and then solve the Y(s) DE.
NOTE
After deriving we get at
Y ( s ) ( s s 2 ) + ( m + 1 s ) Y ( s ) = 0
with solution
Y ( s ) = C 0 ( 1 s ) m s m + 1

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