(eq, func, order, match)
return Eq(C.Integral(r['m2']['coeff']*r['m2'][r['y']]/r['m1'][r['y']],
        (r['y'], None, u)), C.Integral(-r['m1']['coeff']*r['m1'][x]/
        r['m2'][x], x) + C1)
r"""
    Solves separable 1st order differential equations.

    This is any differential equation that can be written as `P(y)
    \tfrac{dy}{dx} = Q(x)`.  The solution can then just be found by
    rearranging terms and integrating: `\int P(y) \,dy = \int Q(x) \,dx`.
    This hint uses :py:meth:`sympy.simplify.simplify.separatevars` as its back
    end, so if a separable equation is not caught by this solver, it is most
    likely the fault of that function.
    :py:meth:`~sympy.simplify.simplify.separatevars` is
    smart enough to do most expansion and factoring necessary to convert a
    separable equation `F(x, y)` into the proper form `P(x)\cdot{}Q(y)`.  The
    general solution is::

        >>> from sympy import Function, dsolve, Eq, pprint
        >>> from sympy.abc import x
        >>> a, b, c, d, f = map(Function, ['a', 'b', 'c', 'd', 'f'])
        >>> genform = Eq(a(x)*b(f(x))*f(x).diff(x), c(x)*d(f(x)))
        >>> pprint(genform)
                     d
        a(x)*b(f(x))*--(f(x)) = c(x)*d(f(x))
                     dx
        >>> pprint(dsolve(genform, f(x), hint='separable_Integral'))
             f(x)
           /                  /
          |                  |
          |  b(y)            | c(x)
          |  ---- dy = C1 +  | ---- dx
          |  d(y)            | a(x)
          |                  |
         /                  /

    Examples
    ========

    >>> from sympy import Function, dsolve, Eq
    >>> from sympy.abc import x
    >>> f = Function('f')
    >>> pprint(dsolve(Eq(f(x)*f(x).diff(x) + x, 3*x*f(x)**2), f(x),
    ... hint='separable', simplify=False))
       /   2       \         2
    log\3*f (x) - 1/        x
    ---------------- = C1 + --
           6                2

    References
    ==========

    - M. Tenenbaum & H. Pollard, "Ordinary Differential Equations",
      Dover 1963, pp. 52

    # indirect doctest
r"""
    Solves separable 1st order differential equations.
r Solves separable 1st order differential equations .
def ode_separable(eq, func, order, match):
    r"""
    Solves separable 1st order differential equations.

    This is any differential equation that can be written as `P(y)
    \tfrac{dy}{dx} = Q(x)`.  The solution can then just be found by
    rearranging terms and integrating: `\int P(y) \,dy = \int Q(x) \,dx`.
    This hint uses :py:meth:`sympy.simplify.simplify.separatevars` as its back
    end, so if a separable equation is not caught by this solver, it is most
    likely the fault of that function.
    :py:meth:`~sympy.simplify.simplify.separatevars` is
    smart enough to do most expansion and factoring necessary to convert a
    separable equation `F(x, y)` into the proper form `P(x)\cdot{}Q(y)`.  The
    general solution is::

        >>> from sympy import Function, dsolve, Eq, pprint
        >>> from sympy.abc import x
        >>> a, b, c, d, f = map(Function, ['a', 'b', 'c', 'd', 'f'])
        >>> genform = Eq(a(x)*b(f(x))*f(x).diff(x), c(x)*d(f(x)))
        >>> pprint(genform)
                     d
        a(x)*b(f(x))*--(f(x)) = c(x)*d(f(x))
                     dx
        >>> pprint(dsolve(genform, f(x), hint='separable_Integral'))
             f(x)
           /                  /
          |                  |
          |  b(y)            | c(x)
          |  ---- dy = C1 +  | ---- dx
          |  d(y)            | a(x)
          |                  |
         /                  /

    Examples
    ========

    >>> from sympy import Function, dsolve, Eq
    >>> from sympy.abc import x
    >>> f = Function('f')
    >>> pprint(dsolve(Eq(f(x)*f(x).diff(x) + x, 3*x*f(x)**2), f(x),
    ... hint='separable', simplify=False))
       /   2       \         2
    log\3*f (x) - 1/        x
    ---------------- = C1 + --
           6                2

    References
    ==========

    - M. Tenenbaum & H. Pollard, "Ordinary Differential Equations",
      Dover 1963, pp. 52

    # indirect doctest

    """
    x = func.args[0]
    f = func.func
    C1 = get_numbered_constants(eq, num=1)
    r = match  # {'m1':m1, 'm2':m2, 'y':y}
    u = r.get('hint', f(x))  # get u from separable_reduced else get f(x)
    return Eq(C.Integral(r['m2']['coeff']*r['m2'][r['y']]/r['m1'][r['y']],
        (r['y'], None, u)), C.Integral(-r['m1']['coeff']*r['m1'][x]/
        r['m2'][x], x) + C1)
def ode_separable ( eq , func , order , match ) : x = func . args [ 0 ] f = func . func C1 = get_numbered_constants ( eq , num = 1 ) r = match # {'m1':m1, 'm2':m2, 'y':y} u = r . get ( 'hint' , f ( x ) ) # get u from separable_reduced else get f(x) return Eq ( C . Integral ( r [ 'm2' ] [ 'coeff' ] * r [ 'm2' ] [ r [ 'y' ] ] / r [ 'm1' ] [ r [ 'y' ] ] , ( r [ 'y' ] , None , u ) ) , C . Integral ( - r [ 'm1' ] [ 'coeff' ] * r [ 'm1' ] [ x ] / r [ 'm2' ] [ x ] , x ) + C1 )