I suspect that doing this the way you're trying is somewhere between extremely (*extremely!*) difficult and impossible. Sage is a massive package comprised of many components, it would be an absolute nightmare to compile for android even if it's technically possible.
This probably leaves you with two real options. The first is to connect to an external sage http server to do your mathematics, as done by (for instance) sage's own android app.
The second (which is probably much simpler and easier for a small project) is to just use sympy, a pure python symbolic mathematics module. This should run easily on android, and has some tools for working with differential equations, though I haven't personally made much use of them. Of course it does a lot less than sage (actually, sage integrates sympy as one of its many components) but it's also much smaller which makes it actually plausible to use directly on a mobile device.
I don't know about your second question about displaying the 'raw code', you would have to play with sympy yourself to understand its capabilities.