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 this kind Show by differentiation and substitution that it has the general solution y cx c 2 and the singular solution y x 2 4 Expla...

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 this kind. Show by differentiation and substitution that it has the general solution y = cx - c²and the singular solution y = x²/4. Explain Fig. 6.