The solution of the D.Exx2+1dydx=y1−x2+x3logx is
y(x2+1)x=14x2logx+x22+C
y2(x2-1)x=12x2logx-14x2+C
y(x2+1)x=12x2logx-x24+C
y(x2-1)x=12logx+x2/2+C
dydx+x2−1xx2+1y=x2logxx2+1I.F.=e∫x2−1xx2+1dx=e∫2xx2+1−1x dx=elogx2+1x=x2+1x Solution of the D.E yx2+1x=∫xlogxdxyx2+1x=logx ∫xdx -∫1x∫xdx dxyx2+1x=x22logx-∫1x·x22dxyx2+1x=x22logx-x24+c