The solution of $y'-y''=2 x$ is:

A. $y=x^2+2 x+2$
B. $y=x^2+2 x+1$
C. $y=x+2$
D. $y=x^2-2 x+1$

Choose the correct answer from the options given below:

A and B only

$y'-y''=2 x$

\( \begin{array}{ll}
\mbox{A.} &y=x^2+2 x+2 &y'=2 x+2 &y''=2 &  &y'-y''=2 x\\
\mbox{B.} &y=x^2+2 x+1 &y'=2 x+2 &y''=2 &  &y'-y''=2 x\\
\mbox{C.} &y=x+2 &y'=1 &y''=0 &  & y'-y''=1\\
\mbox{D.} &y=x^2-2 x+1 &y'=2 x-2 &y''=2 &  & y'-y''=2 x-4\end{array}\)

so option 1