# Initial Value Problem 3rd order DE - using laplace

• August 29th 2009, 10:37 PM
RoyalFlush
Initial Value Problem 3rd order DE - using laplace
$y''' = \begin{cases} t & t < 3 \\ 0 & t \geq 3 \end{cases}$

with $y(0) = 0, y'(0) = 0, y''(0) = 0$. Solve using Laplace Transforms.
• August 30th 2009, 04:10 AM
mr fantastic
Quote:

Originally Posted by RoyalFlush
$y''' = \begin{cases} t & t < 3 \\ 0 & t \geq 3 \end{cases}$

with $y(0) = 0, y'(0) = 0, y''(0) = 0$. Solve using Laplace Transforms.

You could start by noting that $y''' = H(3 - t) \cdot t$ 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.