#1: x = x0 + vt + 1/2 at^2 = 2 - 10t + 1/2 * t^2 * (6t+2)

#2: I remember you've to separate the variables, i.e. y'/y = 3/(2+x) then integrate both sides.

#4: Put y = ae^(bx) then y' = abe^(bx) so yy' = a^2 b e^(2bx) = e^x which means b = 0.5 and a = +- sqrt(0.5). y(0) = 1 seems to be redundant info!