I'm facing the following exercise:
Let $ f_{1},f_{2}: \mathbb{R}\to\mathbb{R}$ be continuous functions. The homogeneous linear differential equation $$ y''(x)+f_{1}(x)\cdot y'(x) + f_{2}(x)\cdot y(x)=0 $$ has the solution $y_{1}:\mathbb{R}\to\mathbb{R}$ given through $ x\mapsto\sqrt{1+x^{2}}$ and having the property to be continuously differentiable twice. The Wronskian is constant (presumably unequal to zero) for each pair of linearly independent solutions to the differential equation. Determine a fundamental system and the functions $ f_{1}$ and $f_{2}$.
Unfortunately, I'm struggling to find access to this exercise. I tried to apply Reduction of order theorem, but I wasn't able to conclude any implications, especially because I don't know how to interpret the fact that the Wronskian is constant.
I would be very thankful if someone could give some help or a hint for a possible approach.