In a letter to Leibnitz, dated May 20, 1715, he revealed the solutions of the
differential equation
x2 y″ = 2y,
which led to three types of curves, viz , parabolas, hyperbolas and a class of
cubic curves This shows how varied the solutions of such innocent looking
differential equation can be From the second half of the twentieth century attention
has been drawn to the investigation of this complicated nature of the solutions of
differential equations, under the heading ‘qualitative analysis of differential
equations’