Verify whether the given equation(y=c1-cos(x+c2)) is a solution to this equation[(d^2y/dx^2)^2 + (dy/dx)^2 - 1 = 0].

Answer 1

I know that sometimes finding the solution is tricky, but surely just taking the derivatives is easy, no?

y = c1-cos(x+c2)
y' = -sin(x+c2)
y" = -cos(x+c2)

(y")^2 + (y')^2 - 1 = 0

sin^2+cos^2 = 1, right?