P1. Put both derivatives =0 and subtract 2 times the first equation from the second to get an equation with only b. Then solve for b and use the result to find a.
P2. Again, both derivatives =0. The first equation becomes a=b. That result transforms the second equation into an equation with only one variable. Solve it.
P3. I'm assuming that A, B, D and E are also constants? Just put that expression =0 and solve for z(t).
P4. Again, the equation is "what you wrote"=0. Just divide both sides with z to simplify the equation.
If you want more help than that, I think you should show us what you've got so far.