Answer
$y=c_1sinx+c_2cosx+sinxln(sinx)-xcosx$
Work Step by Step
$y''+y=cscx$ which has the characteristic equation $t^2+1=0$ with solutions $t=\pm i$
Complementary solution: $y_c=c_1sinx+c_2cosx$
Particular solution: $y_p=sinxln(sinx)-xcosx$
General solution: $y=y_c+y_p=c_1sinx+c_2cosx+sinxln(sinx)-xcosx$
