Updates:
Cc: smichr
Comment #1 on issue 1765 by asmeurer: classify_ode((x**2 +
f(x)**2)*f(x).diff(x) - 2*x*f(x), f(x)) is wrong
http://code.google.com/p/sympy/issues/detail?id=1765
The 1st_linear part used to work. It was broken with this commit:
commit d0906fff0dc21ed69369f3cfb77af358f119ec68
Author: Chris Smith <smi...@gmail.com>
Date: Mon Nov 9 06:02:59 2009 +0545
1686: linear ODE identification
A more robust method is used to identify a
linear ODE. collect() cannot collect on more
than one term, and match doesn't pull together
multiple terms so the added test (a previously
failing expression) is identified by pulling
out the coefficients of the terms of interest
and checking to see that what was collected
reconstructs the original equation.
diff --git a/sympy/solvers/ode.py b/sympy/solvers/ode.py
index 1662aa8..ef71dcb 100755
--- a/sympy/solvers/ode.py
+++ b/sympy/solvers/ode.py
@@ -584,8 +584,16 @@ def classify_ode(eq, func, dict=False):
# We can save a lot of time by skipping these if the ODE isn't 1st
order
# Linear case: a(x)*y'+b(x)*y+c(x) == 0
- r = reduced_eq.match(a*df + b*f(x) + c)
- if r:
+ if eq.is_Add:
+ ind, dep = reduced_eq.as_independent(f)
+ else:
+ u = Symbol('u', dummy=True)
+ ind, dep = (reduced_eq + u).as_independent(f)
+ ind, dep = [tmp.subs(u, 0) for tmp in [ind, dep]]
+ r = {a: dep.coeff(df, expand=False) or 0,
+ b: dep.coeff(f(x), expand=False) or 0,
+ c: ind}
+ if (r[a]*df + r[b]*f(x) + r[c]).expand() - reduced_eq == 0:
r['a'] = a
r['b'] = b
r['c'] = c
diff --git a/sympy/solvers/tests/test_ode.py
b/sympy/solvers/tests/test_ode.py
index 1a05945..57ff0bb 100644
--- a/sympy/solvers/tests/test_ode.py
+++ b/sympy/solvers/tests/test_ode.py
@@ -1055,3 +1055,6 @@ def test_unexpanded_Liouville_ODE():
assert dsolve(eq2, f(x)) in (sol2, sol2s)
assert checkodesol(eq2, f(x), sol2, order=2, solve_for_func=False)[0]
+def test_1686():
+ eq = x + C1*(x + diff(f(x), x) + f(x)) + diff(f(x), x) + f(x) + 2
+ assert classify_ode(eq, f(x)) == ('1st_linear', '1st_linear_Integral')
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