The Problem $y ^ { \prime \prime } + x y y ^ { \prime } = 0 , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 1$

Multiple Choice

The problem $y ^ { \prime \prime } + x y y ^ { \prime } = 0 , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 1$ can be written as a system of two equations as follows.

A) $y ^ { \prime } = u , u ^ { \prime } = x y u , y ( 0 ) = 0 , u ( 0 ) = 0$
B) $y ^ { \prime } = u , u ^ { \prime } = - x y u , y ( 0 ) = 1 , u ( 0 ) = 0$
C) $y ^ { \prime } = u , u ^ { \prime } = x y u , y ( 0 ) = 1 , u ( 0 ) = 0$
D) $y ^ { \prime } = u , u ^ { \prime } = x y u , y ( 0 ) = 0 , u ( 0 ) = 1$
E) $y ^ { \prime } = u , u ^ { \prime } = - x y u , y ( 0 ) = 0 , u ( 0 ) = 1$