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

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.

4 21 12 4 x -3 Particular solutions and singular Fig. 6. solution in Problem 16

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