Martin Rubey <[email protected]> writes:

> Hi there!
>
> I wanted to integrate a second order nonlinear differential equation,
> and fricas responded with the error "no a linear diffeq"...  Is just the
> error message misleading, or is it a bug?

I should add: ")tr" shows that solve indeed calls the solver for
non-linear equations, as I wanted it too.

Martin

> (I admit that I'd be positively surprised if it would have an elementary
> integral...)
>
> Martin
>
> (1) -> D := series([(1/(n+1)*binomial(2*n, n))^2 for n in 0..])$UFPS FRAC 
> POLY INT;
>
>              Type: UnivariateFormalPowerSeries(Fraction(Polynomial(Integer)))
> (2) -> P := 1 - recip D;
>
>              Type: UnivariateFormalPowerSeries(Fraction(Polynomial(Integer)))
> (3) -> Da := recip(1-a*P);
>
>   Type: Union(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))),...)
> (4) -> )expose RECOP
>    RecurrenceOperator is now explicitly exposed in frame frame1 
> (4) -> eq := getEq first guessADE([Da.i for i in 0..50])
>
>    (4)
>            2        3       2      2             3      2  ,,
>      (((16a  - 16a)x  + (- a  + a)x )f(x) + 16a x  - a x )f  (x)
>
>    + 
>             2        3      2       2  ,   2
>      ((- 32a  + 32a)x  + (2a  - 2a)x )f (x)
>
>    + 
>            2        2        2                    2         ,
>      (((32a  - 32a)x  + (- 3a  + 3a)x)f(x) + 32a x  - 3a x)f (x)
>
>    + 
>          3     2           2              3       2           2              2
>      ((4a  - 8a  + 4a)x - a  + 2a - 1)f(x)  + ((8a  - 8a)x + a  - 4a + 3)f(x)
>    + 
>      (4a x + 2a - 3)f(x) + 1
>                                                     Type: Expression(Integer)
> (5) -> f := operator 'f;
>
>                                                           Type: BasicOperator
> (6) -> solve(eq, f, x)
>  
>    >> Error detected within library code:
>    parseLODE: not a linear ordinary differential equation

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