= Solution
{c}
Eliminate the two pure second derivatives by taking $\alpha,\beta$ to be the <roots> of $z^2+2Bz+C=0$. They are distinct <real numbers> exactly when
$$
\boxed{B^2>C,\qquad\alpha=-B+\sqrt{B^2-C},\quad\beta=-B-\sqrt{B^2-C}.}
$$
Thus the required <function> is $H(B)=B^2$. The mixed coefficient becomes $4(C-B^2)\ne0$, so the transformed equation is $y_{\xi\eta}=0$. Integrating once in each coordinate gives
$$
\boxed{y(x,t)=F(x+\alpha t)+G(x+\beta t),}
$$
with arbitrary sufficiently smooth <functions> $F,G$. This is the characteristic form of a strictly <hyperbolic partial differential equation>.
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