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Combining SageMath with LaTeX can be done with:
- SageTeX
- PythonTeX
- texsurgery
You could also have a look into TeXmacs and its SageMath package.
To solve the differential equation:
sage: y = function('y')(x)
sage: de = diff(y, x) == x^3 + x
sage: desolve(de, y)
1/4*x^4 + 1/2*x^2 + _C
