A function $\phi(x)$ is called the singular solution of the differential equation $F(x,y,y')=0,$ if uniqueness of solution is violated at each point of the domain of the equation. Geometrically this means that more than one integral curve with the common tangent line passes through each point $(x_0,y_0).$
Sometimes the weaker definition of the singular solution is used, when the uniqueness of solution of differential equation may be violated only at some points.
In many books, online videos, notes available in the Google, the differential equations $F(x,y,y')=0$ used to find the singular solution are taken as non-linear differential equation.
Is it possible that this differential equation $F(x,y,y')=0$ be linear.
I think the question is now more clear than the previous version.
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