def linear(y_0, y_1, x_0, x_1, k):
    """Returns the particular integral and its derivative for linear load.
    
    y_0, y_1 the ordinates @ the extremes of the loading,
    x_0, x_1 the abscissae @ the extremes of the loading,
    k      the stiffness of the oscillator.

    The returned functions are defined in terms of a new variable,
        csi=x-x_0,
    in the interval 0 <= csi <= x_0.
    """
    y_0, y_1 = y_0/k, y_1/k
    return (lambda x: y_0 + (y_1-y_0)/(x_1-x_0)*x,
            lambda x: (y_1-y_0)/(x_1-x_0))