OIMU 1998 Problem 6

Take the following differential equation: $$3(3+x^2)\frac{dx}{dt}=2(1+x^2)^2e^{-t^2}$$ If $x(0)\leq 1$ , prove that there exists $M>0$ such that $|x(t)|<M$ for all $t\geq 0$ .