Hmm This definitely turns it into a second order?
What form does the second order take? (I'm wondering if I need to try and eliminate that t^2 term in the process)
Differentiate the first equation with respect to t. Then use the first equation and the resultant differential equation to eliminate a variable in the second equation. Which variable that would be would be telling!
try using dy/dt = (dy/dx)(dx/dt)