Consider the problem of a vibrating string, tightly-stretched between

x = 0

and

x = 1

, with a fixed initial position,

f ( x )

, and zero initial velocity. The mathematical problem for the deflection,

u ( x , t )

, is

( \text { with } u ( 0 , t ) = 0 , u ( 1 , t ) = 0 )

\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial u } { \partial t } , u ( x , 0 ) = f ( x ) , u _ { t } ( x , 0 ) = 0

\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial u } { \partial t } = 0 , u ( x , 0 ) = f ( x ) , u _ { t } ( x , 0 ) = 0

\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } , u ( x , 0 ) = f ( x ) , u _ { t } ( x , 0 ) = 0

\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } = 0 , u ( x , 0 ) = f ( x ) , u _ { t } ( x , 0 ) = 0

\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } , u ( x , 0 ) = 0 , u _ { t } ( x , 0 ) = f ( x )

The Value Of L{eterf⁡(t)}\mathcal { L } \left\{ \mathrm { e } ^ { t } \operatorname { erf } ( \sqrt { t } ) \right\}L{eterf(t​)}

Multiple Choice