Solve dydx=yx+1+(y/x)2\frac{dy}{dx} = \frac{y}{x} + \sqrt{1 + (y/x)^2}dxdy=xy+1+(y/x)2 with y(1)=0y(1)=0y(1)=0.
y=xsinh(lnx)y = x \sinh(\ln x)y=xsinh(lnx)
y=x2(x−x−1)y = \frac{x}{2} (x - x^{-1})y=2x(x−x−1)
y=xlnxy = x \ln xy=xlnx
y=x2−1y = \sqrt{x^2-1}y=x2−1