y = a x² + b x + c is a parabola. But, a parabola is just a kind of conic.(adsbygoogle = window.adsbygoogle || []).push({});

All conics are given by a x² + b x y + c y² + d x + e y + f = 0

The same way, the graphic y = f(x), with f(x) satisfying a d²f/dx² + b df/dx + c f = 0, is just a particular graphic of F(x,y) = 0 with F(x,y) satisfying

a d²F/dx² + b d²F/dxdy + c d²F/dy² + d dF/dx + e dF/dy + f F = 0

OBS: a, b, c... are constants.

So, which is the general solution for the PDE above? And, where I can visualize the graphic?

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# Graphic and solution of PDE

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