second derivative of a function equals the function squared Can someone solve the following differential equation for me please?
The second derivative of a function equals the function squared.
Find $y(x)$ if 
$$
\frac{d^2 y}{dx^2} = y^2
$$

How familiar are up with Weierstrass elliptic functions?
Let $\mathcal{P}(x;a,b)$ be that value of $z$ which makes 
$$
\int_{-\infty}^z \frac{1}{\sqrt{4t^3 - at - b}}dt = x
$$ 
This is the Weierstrass $\mathcal{P}$ function.
The general solution to 
$$
\frac{d^2 y}{dx^2} = y^2
$$
is 
$$
y = \sqrt[3]{6} \,\mathcal{P} \left( \frac{x+c_1}{\sqrt[3]{6}}; 0, c_2\right)
$$
where $c_1$ and $c_2$ are constants determined by the initial conditions.
The Weierstrass $\mathcal{P}$ function looks kind of like your top row of front teeth, as seen by a nearsighted dentist.
