A Uniform Beam of Length 10 Has a Concentrated Load $w _ { 0 }$

A uniform beam of length 10 has a concentrated load $w _ { 0 }$ at $x = 5$ . It is embedded at both ends. The boundary value problem for the deflections, $y ( x )$ , for this system is

A) $y ^ { \prime \prime \prime \prime } = E L w _ { 0 } \delta ( x - 5 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ( 10 ) = 0 , y ^ { \prime } ( 10 ) = 0$
B) $y ^ { \prime \prime } = E l w _ { 0 } \delta ( x - 10 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ( 10 ) = 0 , y ^ { \prime } ( 10 ) = 0$
C) $E l y ^ { \prime \prime } = w _ { 0 } \delta ( x - 5 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ( 10 ) = 0 , y ^ { \prime } ( 10 ) = 0$
D) $E L y ^ { \prime \prime \prime } = w _ { 0 } \delta ( x - 5 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ( 10 ) = 0 , y ^ { \prime } ( 10 ) = 0$
E) $E L y ^ { \prime \prime \prime \prime } = w _ { 0 } \delta ( x - 10 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ( 10 ) = 0 , y ^ { \prime } ( 10 ) = 0$