[tex]\dfrac{\mathrm dy}y+ye^{\cos x}\sin x\,\mathrm dx=0[/tex]
[tex]\implies\dfrac{\mathrm dy}{y^2}=-e^{\cos x}\sin x\,\mathrm dx[/tex]
[tex]\displaystyle\int\frac{\mathrm dy}{y^2}=-\int e^{\cos x}\sin x\,\mathrm dx[/tex]
[tex]-\dfrac1y=e^{\cos x}+C[/tex]
[tex]y=-\dfrac1{e^{\cos x}+C}[/tex]
