= Solution
For drift $A_i(x)$ and constant diffusion matrix $b_{ij}$, the <Fokker-Planck equation> is
$$
\frac{\partial P}{\partial t}
=-\frac{\partial}{\partial x_i}(A_iP)
+\frac12\frac{\partial^2}{\partial x_i\partial x_j}(b_{ij}P).
$$
Here
$$
A_1=-x_1+x_2,
\qquad
A_2=-2x_1-x_2,
\qquad
b=I,
$$
so
$$
\boxed{
\frac{\partial P}{\partial t}
=\frac{\partial}{\partial x_1}\bigl[(x_1-x_2)P\bigr]
+\frac{\partial}{\partial x_2}\bigl[(2x_1+x_2)P\bigr]
+\frac12\left(
\frac{\partial^2P}{\partial x_1^2}
+\frac{\partial^2P}{\partial x_2^2}\right)}.
$$
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