y'+y/x=sinx
y=e^-∫1/xdx(c+∫sinx*e^∫1/xdx)
=e^(-lnx)(c+∫sinxe^(lnx)dx)
=1/x(c+∫xsinxdx)
=1/x(c-∫xdcosx)
=1/x(c-xcosx+∫cosxdx)
=1/x(c-xcosx+sinx)
y'+y/x=sinx
y=e^-∫1/xdx(c+∫sinx*e^∫1/xdx)
=e^(-lnx)(c+∫sinxe^(lnx)dx)
=1/x(c+∫xsinxdx)
=1/x(c-∫xdcosx)
=1/x(c-xcosx+∫cosxdx)
=1/x(c-xcosx+sinx)