The initial value problem $x ^ { \prime \prime } - x ^ { \prime } + t x = 0 , x ( 0 ) = 1 , x ^ { \prime } ( 0 ) = 2$ can be rewritten as the system
A) $x ^ { \prime } = x , u ^ { \prime } = u - t x , x ( 0 ) = 1 , u ( 0 ) = 2$
B) $x ^ { \prime } = x , u ^ { \prime } = x - t u , x ( 0 ) = 1 , u ( 0 ) = 2$
C) $x ^ { \prime } = u , u ^ { \prime } = u + t x , x ( 0 ) = 1 , u ( 0 ) = 2$
D) $x ^ { \prime } = u , u ^ { \prime } = x + t u , x ( 0 ) = 1 , u ( 0 ) = 2$
E) $x ^ { \prime } = u , u ^ { \prime } = u - t x , x ( 0 ) = 1 , u ( 0 ) = 2$

Question

Quizplus · Accepted Answer

The second-order differential equation can be rewritten as a system of first-order equations by letting $x' = u$, then $u' = x'' = x' - tx = u - tx$.

The Initial Value Problem x′′−x′+tx=0,x(0)=1,x′(0)=2x ^ { \prime \prime } - x ^ { \prime } + t x = 0 , x ( 0 ) = 1 , x ^ { \prime } ( 0 ) = 2x′′−x′+tx=0,x(0)=1,x′(0)=2

The Initial Value Problem $x ^ { \prime \prime } - x ^ { \prime } + t x = 0 , x ( 0 ) = 1 , x ^ { \prime } ( 0 ) = 2$