NDSolve[{D[u[t, x], t] == 2*x*D[u[t, x], x]+x^2*D[u[t, x], x, x]-u[t,x], u[0, x] == 1.5, u[t, 0] == 2, u[t, 1] == 1}, u, {t, 0, 10}, {x, 0, 1}]

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