Example 4. Find the singular solutions of the differential equation

$$
\left(y^{\prime}\right)^{2}=4 x^{2}
$$
Solution. Differentiating (23) with respect to $y_{1}$:

$$
2 y^{\prime}=0
$$

Excluding $y^{\prime}$ from (23) and (24), we get $x^{2}=0$. The discriminant curve is the y-axis. It is not an integral curve of equation (23), but according to scheme (16) it can be the geometric locus of points of tangency of integral curves.

The solutions of equation (23) are parabolas

$$
y=x^{2}+C, \quad y=-x^{2}+C
$$

and any smooth curves that can be composed from their parts (Fig. 21).

From the drawing, it is clear that the line $x=0$ is indeed the geometric locus of points of tangency of the integral curves of equation (23).