Consider the following system :
$$ \begin{aligned} \frac{d^2t}{d\lambda^2} &= -f\left(t\right)\frac{d t}{d \lambda}\frac{d t}{d \lambda} -A\frac{d g\left(t,x\right)}{d \lambda}\frac{d t}{d \lambda}+ B\frac{\partial g\left(t,x\right)}{\partial t}\left(\frac{d t}{d \lambda}\right)^2 \\ \frac{d^2x}{d\lambda^2} &= -f\left(t\right)\frac{d t}{d \lambda}\frac{d x}{d \lambda} +A\frac{d g\left(t,x\right)}{d \lambda}\frac{d x}{d \lambda} -B\frac{\partial g\left(t,x\right)}{\partial x}\left(\frac{d t}{d \lambda}\right)^2 \end{aligned} $$ Where $f$ depends only on $t$, $g$ depends on $t$ and $x$, and $A$ and $B$ are two constants. Is there a way to rewrite this system without $\lambda$ in order to obtain :
$$\frac{d^2x}{dt^2} =\quad ?$$