refactor(test_ode.py): 1st_exact examples

Mohitbalwani26 · Mohitbalwani26 · commit e578d979e63d · 2020-10-15T23:20:40.000+05:30
diff --git a/sympy/solvers/ode/tests/test_ode.py b/sympy/solvers/ode/tests/test_ode.py
@@ -813,35 +813,6 @@ def test_old_ode_tests():
     assert checkodesol(eq11, sol11, order=1, solve_for_func=False)[0]
 
 
-@slow
-def test_1st_exact1():
-    # Type: Exact differential equation, p(x,f) + q(x,f)*f' == 0,
-    # where dp/df == dq/dx
-    eq1 = sin(x)*cos(f(x)) + cos(x)*sin(f(x))*f(x).diff(x)
-    eq2 = (2*x*f(x) + 1)/f(x) + (f(x) - x)/f(x)**2*f(x).diff(x)
-    eq3 = 2*x + f(x)*cos(x) + (2*f(x) + sin(x) - sin(f(x)))*f(x).diff(x)
-    eq4 = cos(f(x)) - (x*sin(f(x)) - f(x)**2)*f(x).diff(x)
-    eq5 = 2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x)
-    sol1 = [Eq(f(x), -acos(C1/cos(x)) + 2*pi), Eq(f(x), acos(C1/cos(x)))]
-    sol2 = Eq(f(x), exp(C1 - x**2 + LambertW(-x*exp(-C1 + x**2))))
-    sol2b = Eq(log(f(x)) + x/f(x) + x**2, C1)
-    sol3 = Eq(f(x)*sin(x) + cos(f(x)) + x**2 + f(x)**2, C1)
-    sol4 = Eq(x*cos(f(x)) + f(x)**3/3, C1)
-    sol5 = Eq(x**2*f(x) + f(x)**3/3, C1)
-    assert dsolve(eq1, f(x), hint='1st_exact') == sol1
-    assert dsolve(eq2, f(x), hint='1st_exact') == sol2
-    assert dsolve(eq3, f(x), hint='1st_exact') == sol3
-    assert dsolve(eq4, hint='1st_exact') == sol4
-    assert dsolve(eq5, hint='1st_exact', simplify=False) == sol5
-    assert checkodesol(eq1, sol1, order=1, solve_for_func=False)[0]
-    # issue 5080 blocks the testing of this solution
-    # FIXME: assert checkodesol(eq2, sol2, order=1, solve_for_func=False)[0]
-    assert checkodesol(eq2, sol2b, order=1, solve_for_func=False)[0]
-    assert checkodesol(eq3, sol3, order=1, solve_for_func=False)[0]
-    assert checkodesol(eq4, sol4, order=1, solve_for_func=False)[0]
-    assert checkodesol(eq5, sol5, order=1, solve_for_func=False)[0]
-
-
 @slow
 @XFAIL
 def test_1st_exact2_broken():
diff --git a/sympy/solvers/ode/tests/test_single.py b/sympy/solvers/ode/tests/test_single.py
@@ -33,7 +33,7 @@
 
 """
 from sympy import (acos, asin, atan, cos, Derivative, Dummy, diff,
-    E, Eq, exp, I, log, pi, Piecewise, Rational, S, sin, sinh, tan,
+    E, Eq, exp, I, LambertW, log, pi, Piecewise, Rational, S, sin, sinh, tan,
     sqrt, symbols, Ei, erfi)
 
 from sympy.core import Function, Symbol
@@ -318,6 +318,11 @@ def test_nth_algebraic():
     _ode_solver_test(_get_examples_ode_sol_nth_algebraic())
 
 
+@slow
+def test_slow_examples_1st_exact():
+    _ode_solver_test(_get_examples_ode_sol_1st_exact(), run_slow_test=True)
+
+
 @slow
 def test_slow_examples_nth_order_reducible():
     _ode_solver_test(_get_examples_ode_sol_nth_order_reducible(), run_slow_test=True)
@@ -1284,6 +1289,48 @@ def _get_examples_ode_sol_separable():
     }
 
 
+def _get_examples_ode_sol_1st_exact():
+    # Type: Exact differential equation, p(x,f) + q(x,f)*f' == 0,
+    # where dp/df == dq/dx
+    return {
+            'hint': "1st_exact",
+            'func': f(x),
+            'examples':{
+    '1st_exact_01': {
+        'eq': sin(x)*cos(f(x)) + cos(x)*sin(f(x))*f(x).diff(x),
+        'sol': [Eq(f(x), -acos(C1/cos(x)) + 2*pi), Eq(f(x), acos(C1/cos(x)))],
+        'slow': True,
+    },
+
+    '1st_exact_02': {
+        'eq': (2*x*f(x) + 1)/f(x) + (f(x) - x)/f(x)**2*f(x).diff(x),
+        'sol': [Eq(f(x), exp(C1 - x**2 + LambertW(-x*exp(-C1 + x**2))))],
+        'slow': True,
+    },
+
+    '1st_exact_03': {
+        'eq': 2*x + f(x)*cos(x) + (2*f(x) + sin(x) - sin(f(x)))*f(x).diff(x),
+        'sol': [Eq(f(x)*sin(x) + cos(f(x)) + x**2 + f(x)**2, C1)],
+        'slow': True,
+    },
+
+    '1st_exact_04': {
+        'eq': cos(f(x)) - (x*sin(f(x)) - f(x)**2)*f(x).diff(x),
+        'sol': [Eq(x*cos(f(x)) + f(x)**3/3, C1)],
+        'slow': True,
+    },
+
+    '1st_exact_05': {
+        'eq': 2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x),
+        'sol': [Eq(x**2*f(x) + f(x)**3/3, C1)],
+        # 'sol':[Eq(f(x), 2**Rational(1, 3)*(x**2/(-3*C1 + sqrt(9*C1**2 + 4*x**6))**Rational(1, 3) - 2**Rational(1, 3)*(-3*C1 + sqrt(9*C1**2 + 4*x**6))**Rational(1, 3)/2)), Eq(f(x), 2**Rational(1, 3)*(2*x**2/((-1 - sqrt(3)*I)*(-3*C1 + sqrt(9*C1**2 + 4*x**6))**Rational(1, 3)) + 2**Rational(1, 3)*(-3*C1 + sqrt(9*C1**2 + 4*x**6))**Rational(1, 3)/4 + 2**Rational(1, 3)*sqrt(3)*I*(-3*C1 + sqrt(9*C1**2 + 4*x**6))**Rational(1, 3)/4)),
+        # Eq(f(x), 2**Rational(1, 3)*(2*x**2/((-1 + sqrt(3)*I)*(-3*C1 + sqrt(9*C1**2 + 4*x**6))**Rational(1, 3)) + 2**Rational(1, 3)*(-3*C1 + sqrt(9*C1**2 + 4*x**6))**Rational(1, 3)/4 - 2**Rational(1, 3)*sqrt(3)*I*(-3*C1 + sqrt(9*C1**2 + 4*x**6))**Rational(1, 3)/4))],
+        'slow': True,
+    },
+    }
+    }
+
+
 def _get_all_examples():
     all_solvers = [_get_examples_ode_sol_euler_homogeneous(),
     _get_examples_ode_sol_euler_undetermined_coeff(),
