(eq, func, order, match)
return ode_1st_homogeneous_coeff_best(eq, func, order, match)
r"""
    Solves a differential equation with linear coefficients.

    The general form of a differential equation with linear coefficients is

    .. math:: y' + F\left(\!\frac{a_1 x + b_1 y + c_1}{a_2 x + b_2 y +
                c_2}\!\right) = 0\text{,}

    where `a_1`, `b_1`, `c_1`, `a_2`, `b_2`, `c_2` are constants and `a_1 b_2
    - a_2 b_1 \ne 0`.

    This can be solved by substituting:

    .. math:: x = x' + \frac{b_2 c_1 - b_1 c_2}{a_2 b_1 - a_1 b_2}

              y = y' + \frac{a_1 c_2 - a_2 c_1}{a_2 b_1 - a_1
                  b_2}\text{.}

    This substitution reduces the equation to a homogeneous differential
    equation.

    See Also
    ========
    :meth:`sympy.solvers.ode.ode_1st_homogeneous_coeff_best`
    :meth:`sympy.solvers.ode.ode_1st_homogeneous_coeff_subs_indep_div_dep`
    :meth:`sympy.solvers.ode.ode_1st_homogeneous_coeff_subs_dep_div_indep`

    Examples
    ========

    >>> from sympy import Function, Derivative, pprint
    >>> from sympy.solvers.ode import dsolve, classify_ode
    >>> from sympy.abc import x
    >>> f = Function('f')
    >>> df = f(x).diff(x)
    >>> eq = (x + f(x) + 1)*df + (f(x) - 6*x + 1)
    >>> dsolve(eq, hint='linear_coefficients')
    [f(x) == -x - sqrt(C1 + 7*x**2) - 1, f(x) == -x + sqrt(C1 + 7*x**2) - 1]
    >>> pprint(dsolve(eq, hint='linear_coefficients'))
                      ___________                     ___________
                   /         2                     /         2
    [f(x) = -x - \/  C1 + 7*x   - 1, f(x) = -x + \/  C1 + 7*x   - 1]


    References
    ==========

    - Joel Moses, "Symbolic Integration - The Stormy Decade", Communications
      of the ACM, Volume 14, Number 8, August 1971, pp. 558
r"""
    Solves a differential equation with linear coefficients.
r Solves a differential equation with linear coefficients .
def ode_linear_coefficients(eq, func, order, match):
    r"""
    Solves a differential equation with linear coefficients.

    The general form of a differential equation with linear coefficients is

    .. math:: y' + F\left(\!\frac{a_1 x + b_1 y + c_1}{a_2 x + b_2 y +
                c_2}\!\right) = 0\text{,}

    where `a_1`, `b_1`, `c_1`, `a_2`, `b_2`, `c_2` are constants and `a_1 b_2
    - a_2 b_1 \ne 0`.

    This can be solved by substituting:

    .. math:: x = x' + \frac{b_2 c_1 - b_1 c_2}{a_2 b_1 - a_1 b_2}

              y = y' + \frac{a_1 c_2 - a_2 c_1}{a_2 b_1 - a_1
                  b_2}\text{.}

    This substitution reduces the equation to a homogeneous differential
    equation.

    See Also
    ========
    :meth:`sympy.solvers.ode.ode_1st_homogeneous_coeff_best`
    :meth:`sympy.solvers.ode.ode_1st_homogeneous_coeff_subs_indep_div_dep`
    :meth:`sympy.solvers.ode.ode_1st_homogeneous_coeff_subs_dep_div_indep`

    Examples
    ========

    >>> from sympy import Function, Derivative, pprint
    >>> from sympy.solvers.ode import dsolve, classify_ode
    >>> from sympy.abc import x
    >>> f = Function('f')
    >>> df = f(x).diff(x)
    >>> eq = (x + f(x) + 1)*df + (f(x) - 6*x + 1)
    >>> dsolve(eq, hint='linear_coefficients')
    [f(x) == -x - sqrt(C1 + 7*x**2) - 1, f(x) == -x + sqrt(C1 + 7*x**2) - 1]
    >>> pprint(dsolve(eq, hint='linear_coefficients'))
                      ___________                     ___________
                   /         2                     /         2
    [f(x) = -x - \/  C1 + 7*x   - 1, f(x) = -x + \/  C1 + 7*x   - 1]


    References
    ==========

    - Joel Moses, "Symbolic Integration - The Stormy Decade", Communications
      of the ACM, Volume 14, Number 8, August 1971, pp. 558
    """

    return ode_1st_homogeneous_coeff_best(eq, func, order, match)
def ode_linear_coefficients ( eq , func , order , match ) : return ode_1st_homogeneous_coeff_best ( eq , func , order , match )