# Euler's Number!

Calculus Level 4

There is a curve such that the middle point of the normal from any point on the curve to the $$x$$-axis lies on the parabola $$2y^2=x$$. The equation of the curve is:

$y^2 = bx + c + de^{nx}$

for some constants $$b,c,d,n$$, where e is Euler's number.

What is the value of $$b + c + d + n$$?

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