# [Maxima] ode2 problem

Billinghurst, David (RTATECH) David.Billinghurst at riotinto.com
Tue May 5 18:12:37 CDT 2009

```> From: Robert Marik
>
> (%i1) ode2(x+log(y)+(x/y+sin(x))*'diff(y,x), y, x);
> (%o1)                                false
> (%i2)

There are more methods for nonlinear 1st order odes in contrib_ode().
These don't solve the equation either.  In fact, an intermediate
expression becomes to complex for the Lie group method and it hits
an internal error trap.

(%i1) eq:x+log(y)+(x/y+sin(x))*'diff(y,x);
x           dy
(%o1)                    (- + sin(x)) -- + log(y) + x
y           dx

(%i3) contrib_ode(eq,y,x);
I_y not free of y in ode1_a - impossible
2    9          3           8      8
I_y =  - (((36 x  sin (x) - 36 x  cos(x) sin (x)) y
4           7           3    8      7
+ (144 x  cos(x) sin (x) - 144 x  sin (x)) y

.....

+ (36 x   + 268 x   + 216 x   + 249 x ) sin (x) y
12       11       10     2          13      12       11
+ (- 16 x   - 54 x   + 40 x  ) sin (x) y + (x   + 8 x   + 16 x  )
sin(x))
(%o3)                                false

Your equation is complex and probably doesn't have an analytic solution.

You should consider nuumerical or perturbation methods.

David

```