1 | initial version |

[ Not really an answer, but the damn server software refuses this as a comment... ]

I don't understand your beef with `desolve`

's answer :

```
sage: y=function("y")(x)
sage: E1=diff(y(x),x)==4*y(x)/x+x*sqrt(y(x))
sage: S1=desolve(E1,y(x));S1
1/4*(2*_C + log(x))^2*x^4
sage: var("_C")
_C
sage: bool(E1.subs(y(x)==S1).subs(diff(y(x),x)==diff(S1,x)).canonicalize_radical())
True
```

Therefore, S1 *is* a set of solutions of E1 (though possibly not *the* set of solutions of S1, but this is another question).

BTW, both `mathematica`

and `sympy`

give the same answers (modulo presentation and constant's name) :

```
sage: mathematica("Factor[Part[DSolve[D[y[x],x]==4*y[x]/x+x*Sqrt[y[x]],y[x],x],1,1]]")
y[x] -> (x^4*(2*C[1] + Log[x])^2)/4
sage: import sympy
sage: sympy.dsolve(*[sympy.sympify(u) for u in [E1,y(x)]])_sage_()
y(x) == 1/4*(2*C1 + log(x))^2*x^4
```

`algorithm="fricas"`

can't (currently) solve this ODE. Open question : quid of `giac`

?

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