Solution
= Solution
The proposed function has <partial derivatives> $u_t=1$ and $u_{xx}=2\alpha$. Substitution in the <heat equation> requires $1=\alpha$, hence
$$
\boxed{\alpha=1.}
$$
The coefficient $\beta$ remains arbitrary.
= Solution
The proposed function has <partial derivatives> $u_t=1$ and $u_{xx}=2\alpha$. Substitution in the <heat equation> requires $1=\alpha$, hence
$$
\boxed{\alpha=1.}
$$
The coefficient $\beta$ remains arbitrary.