3(a)

The characteristic equation $r^2 - 2 r + 2 = 0$ has roots $1 \pm i$, so a fundamental set of (complex) solutions is $\exp((1+i)x)$ and $\exp((1-i)x)$. For a fundamental set of real solutions, take the real and imaginary parts of one of these: $${\rm e}^x \cos x$$ and $${\rm e}^x \sin x$$.