Proceed as in this example to find a solution of the initial$-$value problem with the given piecewise$-$defined forcing function.

y$^(\text{'}\text{'})+$y$=$f$($x$),$y$(0)=1,$y$^(\text{'})(0)=-1$

where f$($x$)=\{(0,$x$<mn>0</mn><mi>)</mi>$:$\}$

xpi

$0,$x$>3\backslash$pi

y$($x$)=\{(,$x$<mn>0</mn><mi>)</mi>$:$\}$

xpi

$,$x$>3\backslash$pi