Solution to Differential Equation/Examples/Arbitrary Order 2 Degree 3 ODE

Examples of Solutions to Differential Equations
Consider the equation:
 * $(1): \quad y = x^2$

where $x \in \R$.

Then $(1)$ is a solution to the second order ODE:
 * $(2): \quad \paren {y''}^3 + \paren {y'}^2 - y - 3 x^2 - 8 = 0$

defined on the domain $x \in \R$.

Proof
Then: