I have the following 2D heat equation:
$$u_t - \Delta u = e^t$$ where $(x_1, x_2) \in \mathbb{R}^2, t > 0, u(x_1, x_2, 0) = cos(x_1) sin(x_2)$
I am looking to find the general solution $u(x_1, x_2, t)$. I know that it should be the convolution of the heat kernel and the initial data which I'm unsure how to compute