I am looking for mathematical software to help me set up ODEs. Here is an example of what I want to do:
I have $x = f(t)$ and $y = g(y)$ for some specific functions $f$ and $g$ (for example $f(t) = x^2+2x+9$ and $g(t) = sin(t)+e^t$, this details of this are not important)
and I have the following equation:
$\frac{d^2 y}{d x^2} = a$ for some constant $a$ (say $2$ for example)
I could express $\frac{d^2 y}{d x^2} $ in terms of $\frac{d x}{d t} $ and $\frac{d y}{d t} $ and higher derivates by using the chain rule and product rule, however this would be error prone to do by hand (maybe this particular example is not bad, however a more complex example could be worse).
I would like to know about some mathematical software that I could use to set up such problems, for example I might like to have it formulated as $x' = h(x)$ for some vector function $h$.
Please note, I am not asking about software for solving such ODEs, I have been able to find plenty of these, I am specifically interested in software for setting up these problems before solving them. If such software is bundled with software for solving ODEs that is of course quite fine.
Thanks for your comment, I will use mathematica or maple, I wasn't aware they could do this sort of thing. If you want to make this the answer I will accept it.