dsolve unable to solve differential equation

[RituRajSingh878]

In [17]: str(eq)                                                                      
Out[17]: 'Eq(x**7*Derivative(f(x), x) + 5*x**3*f(x)**2 - (2*x**2 + 2)*f(x)**3, 0)'

In [13]: eq                                                                     
Out[13]: 
 7 d             3  2      ⎛   2    ⎞  3       
x ⋅──(f(x)) + 5⋅x ⋅f (x) - ⎝2⋅x  + 2⎠⋅f (x) = 0
   dx                                          

In [14]: classify_ode(eq)                                                       
Out[14]: ('lie_group',)

ode is classified as 'lie_group' but dsolve is not able to solve. It is going into a infinte loop in the line-

sympy/sympy/solvers/ode.py

Line 5826 in d3c1050

r = pdsolve(rpde, func=f(x, y)).rhs

from there I find that this partial differential equation is hanging-

In [15]: rpde                                                         
Out[15]: 
   7 ∂                                                 
  x ⋅──(f(x, y))   ⎛           2  3      3⎞            
     ∂x            ⎜ 3  2   2⋅x ⋅y    2⋅y ⎟ ∂          
- ────────────── + ⎜x ⋅y  - ─────── - ────⎟⋅──(f(x, y)) 
        5          ⎝           5       5  ⎠ ∂y         

In [16]: classify_pde(rpde)                                                     
Out[16]: ('1st_linear_variable_coeff',)
In [8]: pdsolve(rpde)
stuck

I don't know much about pde so if you can help.

[oscarbenjamin]

This kind of error comes up a lot from the Lie Group solvers. There are many places where solve is assumed to return a single solution.

What are the equations that solve has failed on?

Do you know whether the Lie group solver should be able to solve this?

[oscarbenjamin]

Sorry I didn't mean to close it!

[RituRajSingh878]

Ping @oscarbenjamin

[oscarbenjamin]

I'm not sure why you're pinging me...

[RituRajSingh878]

I'm not sure why you're pinging me...

I have edited the issue and it is hanging somewhere in solving pde so If you can solve the issue because I don't know much about pde.

[oscarbenjamin]

I don't know SymPy's PDE code so well myself. The PDE in question looks like one that I would manually solve with the method of characteristics but I don't know if that is implemented in SymPy:
https://en.wikipedia.org/wiki/Method_of_characteristics

[oscarbenjamin]

Also do you know that there is a closed form analytic solution to this ODE?

[RituRajSingh878]

Also do you know that there is a closed form analytic solution to this ODE?

I don't know the solution but it is hanging in solving so It is a problem.

[jksuom]

It is going into a infinte loop

It seems that this is what happens: There is no easy solution for the nonlinear differential equation, and the Lie group method is attempted as a kind of last resort. That will necessitate calling pdsolve for solving a first order partial differential equation. For the solution, pdsolve calls dsolve for solving a suitable ordinary differential equation. That equation is essentially the same as the original equation, only some variable names have changed and the whole equation has been divided by a known function. Hence the same code will be run again ad infinitum.

[oscarbenjamin]

I find the idea of the Lie group method strange. The method of characteristics reduces an PDE to a system of ODEs which seems like a simplification to me. Turning an ODE into a PDE feels like the wrong direction.