hey guys, i'm really struggling with this and need someone to point me in the right direction, any help at all would be greatly appreciated!

Find the general solution of Eq.2 and hence the general solution for y(x). Your answer should have 2 arbitrary constants of integration.

Here are the equation's i've got so far:

1.$\displaystyle \frac{dy}{dx}=\frac{{\rho}g}{T}\int^x_{0}\sqrt{1+\ frac{dy}{dt}^2}dt$

Differentiating both sides of Eq.1 to produce second order ODE for y(x)

$\displaystyle \frac{d^2y}{dx^2}=\frac{{\rho}g}{T}\sqrt{1+\frac{d y}{dx}^2}$

By letting $\displaystyle u=\frac{dy}{dx}$

$\displaystyle \frac{du}{dx}=\frac{{\rho}g}{T}\sqrt{1+u^2}$

2.