2§dy/dx.d^2y/dx^2.dx=? In this problem § denotes integration sign. This problem is assosiatd wid d eqn of SHM

I'm assuming that you want to evaluate the following integral:

2 ∫ (dy / dx)(d²y / dx²) dx

Note that dy/dx = y ' (x) and d²y / dx² = y''(x) :

2 ∫ y'(x) y''(x) dx

Now make a substitution:

u = y'(x)
du = y''(x) dx
dx = [1 / y'' (x)] du

= 2 ∫ u du
= 2[(1/2)u²]
= u²
= [y ' (x)]² + C
= [dy / dx]² + C

Done!