> 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
(%i2) load('contrib_ode)$
(%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