$\displaystyle y''' = \begin{cases} t & t < 3 \\ 0 & t \geq 3 \end{cases}$
with $\displaystyle y(0) = 0, y'(0) = 0, y''(0) = 0$. Solve using Laplace Transforms.
You could start by noting that $\displaystyle y''' = H(3 - t) \cdot t$ where H(t) is the Heaviside function. Now take Laplace transforms in the usual way.
If you need more help, please post what you've done and where you get stuck.