This is linear differential equation and general form is given by ‌
dy
dx
+P(x)y=Q(x) Here P(x)=cot‌x,Q(x)=‌
e2x
sin‌x
Integrating factor, IF =e∫P(x)dx=e∫cot‌x‌d‌x=eln‌sin‌x IF=sin‌x Solution of linear differential equation y(IF)=∫Q(x)IFdx y(sin‌x)=∫‌