# 1D Heat Equation, Non-Insulated Infinite Bar

Using Fourier Transform in $x$, find the solution $u(x,t)$ to the PDE

$u_t = c^2u_{xx} - hu$

with the initial conditions

$u(x,0) = e^{-x^2} (-\infty < x< \infty)$

Could someone guide me through how to set up this problem?

Make the change $v=e^{ht}u$ and get the heat equation for $v$.