Suppose I have an ODE in the form:
$ y'' + p(x)y' + q(x)y = f(x) $
Suppose now that I have obtained the solution to the equation
$ y'' + p(x)y' + q(x)y = 0 $
which is in the form
$ y(x) = c_1 y_1(x) + c_2 y_2(x) $
My textbook suggests that it is possible to use the Wronskian of the solution in order to obtain a solution to the inhomogeneous equation, hence getting the general solution to the equation.
For example, the homogeneous solution to:
$y'' + 6y' + 2y = 1 $
is $ c_1exp(-3+\sqrt 7)x + c_2exp(-3-\sqrt 7)x $
How is then one able to use the Wronskian to obtain the general solution (which I am able to derive ($y_p = 0.5$) by other methods, but not this one).