Answer
$\{\sin x, \cos x\}$ orthogonal basis of solution space.
Work Step by Step
Solve the characteristic equation for the differential equation. $$r^2+1=0$$
Factor and solve for the roots. $$(r^2+1)=0 $$ $$r= i, -i$$
The general equation is equal to $y=C_1 cos x+C_2 sin x$
Therefore, $\{\sin x, \cos x\}$ is a basis for the solution space.
Since, $\sin x$ and $\cos x$ are orthogonal to each other on the point $[-\pi, \pi]$
This implies that $\{\sin x,\cos x\}$ is orthogonal basis of solution space.
