letu=y/xdu/dx = (1/x).dy/dx - (1/x^2)ydy/dx =x[ du/dx + (1/x)u ]/y'=y/x + sec(y/x)x[ du/dx + (1/x)u ] = u + secuxdu/dx =secu∫cosu du = ∫dx/xsinu = ln|x| + Csin(y/x) = ln|x| + Cy = xarcsin[ln|x| + C]
