An ODE may sometimes have an additional solution that cannot be obtained from the general solution and

Question:

An ODE may sometimes have an additional solution that cannot be obtained from the general solution and is then called a singular solution.
The ODE y’2 – xy’ + y = 0 is of the kind. Show by differentiation and substitution that it has the general solution y = cx – c2 and the singular solution y = x2/4. Explain Fig. 6.