Consider the Cauchy problem $u_t = u_{xx} - a$ for $-\infty < x < \infty$, $t > 0$ with $a$ being a constant. $u(x,0) = H(x)$ where $H(x)$ is the Heaviside function. Solve this using linearity and Duhamel's principle.
I tried using Duhamel's principle, but I get the error function and my professor said the answer will not include the error function