Determine the solution of y′=yx+1y' = \frac{y}{x} + 1y′=xy+1 with y(1)=1y(1) = 1y(1)=1.
y=xy = xy=x
y=x2+1y = x^2 + 1y=x2+1
y=xlnx+xy = x \ln x + xy=xlnx+x
y=xlnxy = x \ln xy=xlnx