# calculus – Differential equations considering the elliptic integrals of the second type.

How can I show that the elliptical integral of the second type

E (x) = $$int_0 ^ frac { pi} {2} sqrt {1-x ^ 2sin ^ 2 (t)} dt$$

satisfies the equation

E & # 39; (x) * ($$x ^ 2 -1) (x)$$ + E & # 39; (x) ($$x ^ 2-1$$) – E (x) * x

where E, e are respectively the first and second derivatives?