Find the value $ofy(x)={\displaystyle \underset{0}{\overset{}{}}}{e}^{-\frac{t^2}{2}}cos(\frac{x^2}{2t^2})dt.$ This $is$ easy once I give

the hints. $(Please$ don't ask for the motivation :$p).$ And here $wego$:$y(x)$ satisfies the $DE{y}^{\text{'}\text{'}\text{'}\text{'}}(x)+y(x)=0.$

$(b)$ Write the general solution.

$(c)$ Find the final answer $y(0)=\sqrt[\phantom{2}]{\frac{}{2}},y^{\text{'}}(0)=-\sqrt[\phantom{2}]{\frac{}{2}},y^{\text{'}\text{'}}(0)=0,y^{\text{'}\text{'}\text{'}}(0)=\frac{\sqrt[\phantom{2}]{}}{2}$