Solution of differential equation dydx+xsin2⁡y=sin⁡ycos⁡y is

dydx+xsin2⁡y=sin⁡ycos⁡ycos⁡ec2ydydx+x=cot⁡y Let −cot⁡y=vdvdx+v=xIF =e∫1dx=exsol: vex=∫exx dx∴ −cot⁡y⋅ex=x∫exdx-∫1∫exdxdx⇒cot⁡y=(x−1)+Ce−x