Solve the boundary value problem (BVP) 1/r d/(dr)(r (du)/(dr))=1, u(1) = 0, u(2) = 0

Ashlynn Hale

Ashlynn Hale

Answered question

2022-08-05

Solve the boundary value problem (BVP)
1 r d d r ( r d u d r ) = 1 , u ( 1 ) = 0 , u ( 2 ) = 0

Answer & Explanation

heiftarab

heiftarab

Beginner2022-08-06Added 10 answers

1 r d d r ( r , d u d r ) = 1
1 r ( r ) d u d r + 1 r r d 2 u d r 2 = 1
1 r d u d r + d 2 u d r 2 = 1
u ( r ) = r 2 4 + c 1 + c 2 ln ( r )
u(1) = 0
0 = 1 4 + c 1 + 0 c 1 = 1 4
u(2)=0
0 = 1 + c 1 + c 2 ln ( 2 ) c 2 ln ( 2 ) = c 1 c 2 ln ( 2 ) = 1 4
c 2 = 1 4 ln ( 2 ) = 1 ln ( 16 )
u ( r ) = r 2 4 + 1 4 + 1 ln ( 16 ) ln ( r )

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