The solution of dydx=yx+tan(yx).
dydx=gn+tan(yx)Itishomogenouous diffenrential equationLety=√x⇒dydx=√+xdvdxandputindifferentialequation⇒√+xdvdx=√+tanv⇒xdvdx=tanv⇒∫dvtanv=∫dxx⇒∫secv=logx+c⇒log|secv=tanv|logxc⇒log∣∣secyx+tanyx∣∣=logxc∣∣secyx+tanyx∣∣=xcAns.