Solving Differential Equations with Mathematica's Solver
(continued from last page...)
Your session should have gone something like this:
DSolve[x y[x] + y[x]^2 + x^2 - x^2 y'[x] == 0, y[x], x]
{{y[x] → x Tan[C[1] + Log[x]]}}
So Mathematica has little trouble handling homogeneous differential equations, (or at least no trouble with this one!) In early versions of Mathematica, the above command would have failed to work. Wolfram Research has refined the algorithms its flagship software uses since then, and continues to do so!
...moving on to the next challenge...
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