differential equation representation

Question

I'm trying to manipulate with differential equation system using sympy:

from sympy import symbols, Function
t = symbols('t')

x_2 = Function('x_2')
x_3 = Function('x_3')

eq = x_3(t).diff(t) + x_2(t).diff(t)
eq1 = eq.subs(x_2(t), x_3(t) + x_3(t).diff(t))

and the answer is:

but I need result in form:

I try to use

eq1.simplify()

but result is same.

How can i get this? Thanks.

Answer 1

You can use doit:

In [2]: eq1                                                                                                                       
Out[2]: 
d ⎛        d        ⎞   d        
──⎜x₃(t) + ──(x₃(t))⎟ + ──(x₃(t))
dt⎝        dt       ⎠   dt       

In [3]: eq1.doit()                                                                                                                
Out[3]: 
                2       
  d            d        
2⋅──(x₃(t)) + ───(x₃(t))
  dt            2       
              dt