Given a variable $x\in[-L,L]$ with $L\in \mathbb{R}$, first consider a generic homogeneous second order differential equation with potential $V(x)$:

$$\left(\frac{d^2}{dx^2}+V(x)\right)f(x)=0$$

Let $f_1 (x)$ and $f_2 (x)$ be two known linearly independent solutions of the homogeneous system. Now consider adding a small constant inhomogeneity $c<<1$ to the differential equation:

$$\left(\frac{d^2}{dx^2}+V(x)\right)f(x)=c$$

Knowing $f_1 (x)$ and $f_2 (x)$, is there any procedure to approximate the solution of the inhomogeneous system using the fact that $c<<1$, without having to actually solve it?