Find d^2y/dx^2. e^ey +x = 4y

Question

d^2y/dx^2 = ?

Answer 1

e^ey +x = 4y

1. Differentiate both sides w.r.t x assuming that y=y(x)

e^ey e*dy/dx +1 = 4dy/dx

(e^(ey+1)-4)dy/dx = -1 ,

From the last equation express dy/dx:

dy/dx=1/(4-e^(ey+1))

Differentiate again w.r.t x. (again assuming y=y(x)):

Any difficulties, let me know.